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Dissertations / Theses on the topic 'Invariant subspaces'
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Adams, Lynn I. "Classifying Triply-Invariant Subspaces." University of Akron / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121.
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Mahvidi, Ali. "Invariant subspaces of composition operators." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0020/NQ45739.pdf.
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POSTERNAK, REGINA. "INVARIANT SUBSPACES FOR HIPONORMAL OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2002. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3338@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROO problema do subespaço invariante consiste na seguinte pergunta: será que todo operador (i.e., transformação linear limitada) atuando em um espaço de Hilbert separável (complexo de dimensão infinita) tem subespaço invariante nãotrivial? Este é, possivelmente, o mais importante problema em aberto na teoria de operadores. Em particular, o problema do subespaço invariante permanece em aberto (pelo menos até a presente data) para operadores hiponormais, ou seja, ainda não se sabe se todo operador hiponormal (atuando em um espaço de Hilbert complexo separável) tem subespaço invariante não-trivial. O objetivo desta dissertação é apresentar, de maneira unificada, um levantamento sobre subespaços invariantes para operadores hiponormais. Inicialmente, o problema do subespaço invariante é abordado em sua forma geral (sem restrição a classes de operadores) onde diversos resultados clássicos são expostos. Em seguida, o problema específico de se encontrar subespaços invariantes para operadores hiponormais é apresentado de maneira sistemática. Em particular, investigamos propriedades do espectro de um operador hiponormal que não tenha subespaço invariante não trivial.
The invariant subspace problem is: does every operator acting on an infinite-dimensional complex separable Hilbert space have a nontrivial invariant subspace? This is, probably, the most important open question in the operator theory. In particular, the problem of the invariant subspace remains open (at least until now) for hyponormal operators, that is, it is still unknown whether every hyponormal operator (on a complex separable Hilbert space) has a nontrivial invariant subspace. The purpose of these dissertation is to present, in an unified way, a survey on invariant subspaces for hyponormal operators. At first, the invariant subspace problem is posed in a general form (without any restriction on the operator classes), where some of classical results are discussed. Secondly, the specific problem of finding invariant subspaces for hyponormal operators is presented in a systematic way and, in particular, we show some characteristics of the spectrum of a hyponormal operator with no nontrivial invariant subspace.
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Mehrmann, Volker, and Hongguo Xu. "Lagrangian invariant subspaces of Hamiltonian matrices." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501133.
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The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and sufficient conditions are given in terms of the Jordan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Hermitian solutions of continuous time algebraic Riccati equations.
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Wojtasinski, Justyna Agata. "Classifying Triply-Invariant Subspaces for p=3." Akron, OH : University of Akron, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=akron1209134757.
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Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2008."May, 2008." Title from electronic thesis title page (viewed 07/12/2008) Advisor, Jeffrey M. Riedl; Faculty Readers, Ethel Wheland, Stuart Clay; Department Chair, Joseph Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.
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Smith, Rachael Caroline. "Spectral densities and invariant subspaces of operators." Thesis, University of Leeds, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432300.
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Schulze, Bert-Wolfgang, Anton Savin, and Boris Sternin. "Elliptic operators in subspaces and the eta invariant." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2549/.
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The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.
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Lücking, Simon [Verfasser]. "The Daugavet Property and Translation-Invariant Subspaces / Simon Lücking." Berlin : Freie Universität Berlin, 2014. http://d-nb.info/1054163154/34.
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Jiang, Jiaosheng. "Bounded operators without invariant subspaces on certain Banach spaces." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3037506.
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Hayakawa, Yoshikazu, and D. ŠILJAK Dragoslav. "On almost invariant subspaces of structural systems and decentralized control." IEEE, 1988. http://hdl.handle.net/2237/6854.
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Byers, R., C. He, and V. Mehrmann. "The Matrix Sign Function Method and the Computation of Invariant Subspaces." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800619.
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A perturbation analysis shows that if a numerically stable
procedure is used to compute the matrix sign function, then it is competitive
with conventional methods for computing invariant subspaces.
Stability analysis of the Newton iteration improves an earlier result of Byers
and confirms that ill-conditioned iterates may cause numerical
instability. Numerical examples demonstrate the theoretical results.
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Yavuz, Onur. "Invariant subspaces for Banach space operators with a multiply connected spectrum." [Bloomington, Ind.] : Indiana University, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3219888.
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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2006."Title from dissertation home page (viewed June 27, 2007)." Source: Dissertation Abstracts International, Volume: 67-06, Section: B, page: 3174. Adviser: Hari Bercovici.
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Sutton, Daniel Joseph. "Structure of Invariant Subspaces for Left-Invertible Operators on Hilbert Space." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/28807.
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This dissertation is primarily concerned with studying the invariant subspaces of left-invertible, weighted shifts, with generalizations to left-invertible operators where applicable. The two main problems that are researched can be stated together as When does a weighted shift have the one-dimensional wandering subspace property for all of its closed, invariant subspaces? This can fail either by having a subspace that is not generated by its wandering subspace, or by having a subspace with an index greater than one. For the former we show that every left-invertible, weighted shift is similar to another weighted shift with a residual space, with respect to being generated by the wandering subspace, of dimension $n$, where $n$ is any finite number. For the latter we derive necessary and sufficient conditions for a pure, left-invertible operator with an index of one to have a closed, invariant subspace with an index greater than one. We use these conditions to show that if a closed, invariant subspace for an operator in a class of weighted shifts has a vector in $l^1$, then it must have an index equal to one, and to produce closed, invariant subspaces with an index of two for operators in another class of weighted shifts.Ph. D.
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Langendörfer, Sebastian [Verfasser], and Jörg [Akademischer Betreuer] Eschmeier. "On unitarily invariant subspaces and Cowen-Douglas theory : characterization of Toeplitz operators, Wold decomposition type theorems and fiber dimension for invariant subspaces / Sebastian Langendörfer ; Betreuer: Jörg Eschmeier." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2019. http://d-nb.info/1196090149/34.
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Langendörfer, Sebastian Verfasser], and Jörg [Akademischer Betreuer] [Eschmeier. "On unitarily invariant subspaces and Cowen-Douglas theory : characterization of Toeplitz operators, Wold decomposition type theorems and fiber dimension for invariant subspaces / Sebastian Langendörfer ; Betreuer: Jörg Eschmeier." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2019. http://nbn-resolving.de/urn:nbn:de:bsz:291--ds-287558.
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Savin, Anton, and Boris Sternin. "Elliptic operators in even subspaces." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2546/.
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An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems.
A connection with Gilkey's theory of η-invariants is established.
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Savin, Anton, and Boris Sternin. "Elliptic operators in odd subspaces." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2547/.
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An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems.
A connection with Gilkey's theory of η-invariants is established.
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Heck, Larry Paul. "A subspace approach to the auomatic design of pattern recognition systems for mechanical system monitoring." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/15016.
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Felix, Christina M. "Classification of Doubly-Invariant Subgroups for p=2." Akron, OH : University of Akron, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=akron1207936688.
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Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2008."May, 2008." Title from electronic thesis title page (viewed 07/12/2008) Advisor, Jeffrey M. Riedl; Faculty Readers, William S. Clary, Ethel R. Wheland; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.
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Caglar, Mert. "Invariant Subspaces Of Positive Operators On Riesz Spaces And Observations On Cd0(k)-spaces." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606391/index.pdf.
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The present work consists of two main parts. In the first part, invariant subspaces of positive operators or operator families on locally convex solid Riesz spaces are examined. The concept of a weakly-quasinilpotent operator on a locally convex solid Riesz space has been introduced and several results that are known for a single operator on Banach lattices have been generalized to families of positive or close-to-them operators on these spaces.
In the second part, the so-called generalized Alexandroff duplicates are studied and CDsigma, gamma(K, E)-type spaces are investigated. It has then been shown that the space CDsigma, gamma(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff duplicate of K.
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Mkhaliphi, Mkhuseli Bruce. "Reconstruction of Functions From Non-uniformly Distributed Sampled Data in Shift-Invariant Frame Subspaces." Master's thesis, Faculty of Engineering and the Built Environment, 2018. http://hdl.handle.net/11427/30079.
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The focus of this research is to study and implement efficient iterative reconstruction algorithms. Iterative reconstruction algorithms are used to reconstruct bandlimited signals in shift-invariant L2 subspaces from a set of non-uniformly distributed sampled data. The Shannon-Whittaker reconstruction formula commonly used in uniform sampling problems is insufficient in reconstructing function from non-uniformly distributed sampled data. Therefore new techniques are required. There are many traditional approaches for non-uniform sampling and reconstruction methods where the Adaptive Weights (AW) algorithm is considered to be the most efficient. Recently, the Partitions of Unity (PoU) algorithm has been suggested to outperform the AW although there has been much literature covering its numerical performance. A study and analysis of the implementation of the Adaptive Weights (AW) and Partitions of Unity (PoU) reconstruction methods is conducted. The algorithms consider the missing data problem, defined as reconstructing continuous-time (CT) signals from non-uniform samples which resulted from missing samples on a uniform grid. Mainly, the algorithms convert the non-uniform grid to a uniform grid. The implemented iterative methods construct CT bandlimited functions in frame subspaces. Bandlimited functions are considered to be a superposition of basis functions, named frames. PoU is a variation of AW, they differ by the choice of frame because each frame produces a different approximation operator and convergence rate. If efficiency is defined as the norm convergence and computational time of an algorithm, then among the two methods, discussed, the PoU method is more efficient. The AW method is slow and converged to a higher error than that of the PoU. However, AW compensates for its slowness and less accuracy by being convergent and robust for large sampling gaps and less sensitive to the sampling irregularities. The impact of additive white Gaussian noise on the performance of the two algorithms is also investigated. The numerical tools utilized in this research consist of the theory of discrete irregular sampling, frames, and iterative techniques. The developed software provides a platform for sampling signals under non-ideal conditions with real devices.
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Dietl, Guido K. E. "Linear estimation and detection in Krylov subspaces : with ... 11 tables /." Berlin [u.a.] : Springer, 2007. http://www.gbv.de/dms/ilmenau/toc/522153062.PDF.
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Savin, Anton, and Boris Sternin. "Pseudodifferential subspaces and their applications in elliptic theory." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2993/.
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The aim of this paper is to explain the notion of subspace defined by means
of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah–Patodi–Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.
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Toolan, Timothy M. "Advances in sliding window subspace tracking /." View online ; access limited to URI, 2005. http://0-wwwlib.umi.com.helin.uri.edu/dissertations/dlnow/3206257.
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Hokamp, Samuel A. "Weak*-Closed Unitarily and Moebius Invariant Spaces of Bounded Measurable Functions on a Sphere." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562943150719334.
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Georgescu, Magdalena. "On the Similarity of Operator Algebras to C*-Algebras." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2932.
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This is an expository thesis which addresses the requirements for an operator algebra to be similar to a C*-algebra. It has been conjectured that this similarity condition is equivalent to either amenability or total reductivity; however, the problem has only been solved for specific types of operators. We define amenability and total reductivity, as well as present some of the implications of these properties. For the purpose of establishing the desired result in specific cases, we describe the properties of two well-known types of operators, namely the compact operators and quasitriangular operators. Finally, we show that if A is an algebra of compact operators or of triangular operators then A is similar to a C* algebra if and only if it has the total reduction property.
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Overmoyer, Kate. "Applications of Entire Function Theory to the Spectral Synthesis of Diagonal Operators." Bowling Green State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1305826657.
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Maree, Johannes Philippus. "Fault detection for the Benfield process using a closed-loop subspace re-identification approach." Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-11262009-224053/.
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Thesis (M.Eng.(Faculty of Engineering, The Built Environment and Information Technology))--University of Pretoria, 2009.Abstracts in English and Afrikaans. Includes bibliographical references (leaves 180-187).
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Barbian, Christoph [Verfasser], and Jörg [Akademischer Betreuer] Eschmeier. "Beurling-type representation of invariant subspaces in reproducing kernel Hilbert spaces / Christoph Barbian. Betreuer: Jörg Eschmeier." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2011. http://d-nb.info/1051285119/34.
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Deters, Ian Nathaniel. "On The Cyclicity And Synthesis Of Diagonal Operators On The Space Of Functions Analytic On A Disk." Bowling Green State University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1236617862.
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Liang, Xiaoming. "A class of weighted Bergman spaces, reducing subspaces for multiple weighted shifts, and dilatable operators." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/39164.
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This thesis consists of four chapters. Chapter 1 contains the preliminaries. We give the background, notation and some results needed for this work, and we describe our main results of this thesis.
In Chapter 2 we will introduce a class of weighted Bergman spaces. We then will discuss some properties about the multiplication operator, Mz , on them. We also characterize the dual spaces of these weighted Bergman spaces.
In Chapter 3 we will characterize the reducing subspaces of multiple weighted shifts. The reducing subspaces of the Bergman and the Dirichlet shift of multiplicity N are portrayed from this characterization.
In Chapter 4 we will introduce the class of super-isometrically dilatable operators and describe their elementary properties. We then will discuss an equivalent description of the invariant subspace lattice for the Bergman shift. We will also discuss the interpolating sequences on the bidisk. Finally, we will examine a special class of super-isometrically dilatable operators. One corollary of this work is that we will prove that the compression of the Bergman shift on two compliments of two invariant subspaces are unitarily equivalent if and only if the two invariant subspaces are equal.Ph. D.
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Medina, Enrique A. "Linear Impulsive Control Systems: A Geometric Approach." Ohio : Ohio University, 2007. http://www.ohiolink.edu/etd/view.cgi?ohiou1187704023.
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Leon, Ralph Daniel. "Module structure of a Hilbert space." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2469.
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This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas.
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PORTELLA, JOAO ANTONIO ZANNI. "REMARKS ABOUT THE INVARIAN SUBSPACE PROBLEM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2011. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=17402@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOO Problema do Subespaço Invariante é a questão em aberto mais importante em Teoria de Operadores. Apesar de existirem diversos resultados parciais, a questão continua em aberto para classes de operadores definidas em espaços de Hilbert complexos separáveis de dimensão infinita. No caso de uma resposta positiva, este pode ser o início de uma teoria geral para a estrutura de operadores em espaços de Hilbert. Se apresentado um contra-exemplo, então o mesmo pode dar origem a diversos teoremas de aproximação. Este trabalho tem como objetivo realizar um levantamento dos principais resultados relativos a essa questão, e apresentar um exemplo de como poderia ser o espectro de um operador hiponormal (em um espaço de Hilbert complexo separável de dimensão infinita) que não tivesse subespaço invariante não trivial (caso tal operador exista).
The Invariant Subspace Problem is the most important open question in Operator Theory. Although, there are many partial results, the question remains open for operators on complex, infinite-dimensional, separable Hilbert spaces. To prove that every operator has a non-trivial invariant subspace might be the beginning of a general structure theory for Hilbert space operators. On the other hand, a counterexample would may yield a number of approximation theorems. In this work we present a survey the Invariant Subspace Problem, and in addition we show also how it might be the spectrum of a hyponormal operator (on a complex separable infinitedimensional Hilbert space) which had no nontrivial invariant subspace.
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Pence, Zachary. "Metric Spectral Theory and the Invariant Subspace Problem." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-453223.
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Vitório, Henrique de Barros Correia. "A geometria de curvas fanning e de suas reduções simpléticas." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306819.
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Orientadores: Carlos Eduardo Durán Fernandez, Marcos Benevenutto JardimTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-16T11:28:16Z (GMT). No. of bitstreams: 1 Vitorio_HenriquedeBarrosCorreia_D.pdf: 1074812 bytes, checksum: e23ca71f5e87d6990c05425cdcb87bee (MD5) Previous issue date: 2010
Resumo: A presente tese dá continuidade ao recente trabalho de J.C . Álvarez e C.E. Durán acerca dos invariantes geométricos de uma classe genérica de curvas em variedades de Grassmann, ditas "curvas fanning". Mais precisamente, considera-se como tais curvas de planos lagrangeanos comportam-se mediante uma redução simplética, e conclui-se a existência de dois novos invariantes que desempenham um papel fundamental neste contexto, mais notavelmente a maneira pela qual eles generalizam as bem conhecidas fórmulas de O'Neill para submersões isométricas
Abstract: The present thesis gives continuity to the recent work of J.C. Álvarez e C.E. Durán about the geometric invariants of a generic class of curves in the Grassmann manifolds, called "fanning curves". More precisely, we look at how such curves of lagrangean planes behave under a symplectic reduction, and establish the existence of two new invariants which play a fundamental role in that context, more notably the way they generalize the well known O'Neill's formulas for isometric submersions
Doutorado
Matematica
Doutor em Matemática
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Chen, Yahao. "Geometric analysis of differential-algebraic equations and control systems : linear, nonlinear and linearizable." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR04.
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Dans la première partie de cette thèse, nous étudions les équations différentielles algébriques (en abrégé EDA) linéaires et les systèmes de contrôles linéaires associés (en abrégé SCEDA). Les problèmes traités et les résultats obtenus sont résumés comme suit : 1. Relations géométriques entre les EDA linéaires et les systèmes de contrôles génériques SCEDO. Nous introduisons une méthode, appelée explicitation, pour associer un SCEDO à n'importe quel EDA linéaire. L'explicitation d'une EDA est une classe des SCEDO, précisément un SCEDO défini, à un changement de coordonnées près, une transformation de bouclage près et une injection de sortie près. Puis nous comparons les « suites de Wong » d'une EDA avec les espaces invariants de son explicitation. Nous prouvons que la forme canonique de Kronecker FCK d'une EDA linéaire et la forme canonique de Morse FCM d'un SCEDO, ont une correspondance une à une et que leurs invariants sont liés. De plus, nous définissons l'équivalence interne de deux EDA et montrons sa particularité par rapport à l'équivalence externe en examinant les relations avec la régularité interne, i.e., l'existence et l'unicité de solutions. 2. Transformation d'un SCEDA linéaire vers sa forme canonique via la méthode d'explicitation avec des variables de driving. Nous étudions les relations entre la forme canonique par bouclage FCFB d'un SCEDA proposée dans la littérature et la forme canonique de Morse pour les SCEDO. Premièrement, dans le but de relier SCEDA avec les SCEDO, nous utilisons une méthode appelée explicitation (avec des variables de driving). Cette méthode attache à une classe de SCEDO avec deux types d'entrées (le contrôle original et le vecteur des variables de driving) à un SCEDA donné. D'autre part, pour un SCEDO linéaire classique (sans variable de driving) nous proposons une forme de Morse triangulaire FMT pour modifier la construction de la FCM. Basé sur la FMT nous proposons une forme étendue FMT et une forme étendue de FCM pour les SCEDO avec deux types d'entrées. Finalement, un algorithme est donné pour transformer un SCEDA dans sa FCFB. Cet algorithme est construit sur la FCM d'un SCEDO donné par la procédure d'explicitation. Un exemple numérique illustre la structure et l'efficacité de l'algorithme. Pour les EDA non linéaires et les SCEDA (quasi linéaires) nous étudions les problèmes suivants : 3. Explicitations, analyse externe et interne et formes normales des EDA non linéaires. Nous généralisons les deux procédures d'explicitation (avec ou sans variables de driving) dans le cas des EDA non linéaires. L'objectif de ces deux méthodes est d'associer un SCEDO non linéaire à une EDA non linéaire telle que nous puissions l'analyser à l'aide de la théorie des EDO non linéaires. Nous comparons les différences de l'équivalence interne et externe des EDA non linéaires en étudiant leurs relations avec l'existence et l'unicité d'une solution (régularité interne). Puis nous montrons que l'analyse interne des EDA non linéaire est liée à la dynamique nulle en théorie classique du contrôle non linéaire. De plus, nous montrons les relations des EDAS de forme purement semi-explicite avec les 2 procédures d'explicitations. Finalement, une généralisation de la forme de Weierstrass non linéaire FW basée sur la dynamique nulle d'un SCEDO non linéaire donné par la méthode d'explicitation est proposéeIn the first part of this thesis, we study linear differential-algebraic equations (shortly, DAEs) and linear control systems given by DAEs (shortly, DAECSs). The discussed problems and obtained results are summarized as follows. 1. Geometric connections between linear DAEs and linear ODE control systems ODECSs. We propose a procedure, named explicitation, to associate a linear ODECS to any linear DAE. The explicitation of a DAE is a class of ODECSs, or more precisely, an ODECS defined up to a coordinates change, a feedback transformation and an output injection. Then we compare the Wong sequences of a DAE with invariant subspaces of its explicitation. We prove that the basic canonical forms, the Kronecker canonical form KCF of linear DAEs and the Morse canonical form MCF of ODECSs, have a perfect correspondence and their invariants (indices and subspaces) are related. Furthermore, we define the internal equivalence of two DAEs and show its difference with the external equivalence by discussing their relations with internal regularity, i.e., the existence and uniqueness of solutions. 2. Transform a linear DAECS into its feedback canonical form via the explicitation with driving variables. We study connections between the feedback canonical form FBCF of DAE control systems DAECSs proposed in the literature and the famous Morse canonical form MCF of ODECSs. In order to connect DAECSs with ODECSs, we use a procedure named explicitation (with driving variables). This procedure attaches a class of ODECSs with two kinds of inputs (the original control input and the vector of driving variables) to a given DAECS. On the other hand, for classical linear ODECSs (without driving variables), we propose a Morse triangular form MTF to modify the construction of the classical MCF. Based on the MTF, we propose an extended MTF and an extended MCF for ODECSs with two kinds of inputs. Finally, an algorithm is proposed to transform a given DAECS into its FBCF. This algorithm is based on the extended MCF of an ODECS given by the explication procedure. Finally, a numerical example is given to show the structure and efficiency of the proposed algorithm. For nonlinear DAEs and DAECSs (of quasi-linear form), we study the following problems: 3. Explicitations, external and internal analysis, and normal forms of nonlinear DAEs. We generalize the two explicitation procedures (with or without driving variable) proposed in the linear case for nonlinear DAEs of quasi-linear form. The purpose of these two explicitation procedures is to associate a nonlinear ODECS to any nonlinear DAE such that we can use the classical nonlinear ODE control theory to analyze nonlinear DAEs. We discuss differences of internal and external equivalence of nonlinear DAEs by showing their relations with the existence and uniqueness of solutions (internal regularity). Then we show that the internal analysis of nonlinear DAEs is closely related to the zero dynamics in the classical nonlinear control theory. Moreover, we show relations of DAEs of pure semi-explicit form with the two explicitation procedures. Furthermore, a nonlinear generalization of the Weierstrass form WE is proposed based on the zero dynamics of a nonlinear ODECS given by the explicitation procedure
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Guan, Yu. "Covariate-invariant gait recognition using random subspace method and its extensions." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/67147/.
Full textAbstract:
Compared with other biometric traits like fingerprint or iris, the most significant advantage of gait is that it can be used for remote human identification without cooperation from the subjects. The technology of gait recognition may play an important role in crime prevention, law enforcement, etc. Yet the performance of automatic gait recognition may be affected by covariate factors such as speed, carrying condition, elapsed time, shoe, walking surface, clothing, camera viewpoint, video quality, etc. In this thesis, we propose a random subspace method (RSM) based classifier ensemble framework and its extensions for robust gait recognition. Covariates change the human gait appearance in different ways. For example, speed may change the appearance of human arms or legs; camera viewpoint alters the human visual appearance in a global manner; carrying condition and clothing may change the appearance of any parts of the human body (depending on what is being carried/wore). Due to the unpredictable nature of covariates, it is difficult to collect all the representative training data. We claim overfitting may be the main problem that hampers the performance of gait recognition algorithms (that rely on learning). First, for speed-invariant gait recognition, we employ a basic RSM model, which can reduce the generalisation errors by combining a large number of weak classifiers in the decision level (i.e., by using majority voting). We find that the performance of RSM decreases when the intra-class variations are large. In RSM, although weak classifiers with lower dimensionality tend to have better generalisation ability, they may have to contend with the underfitting problem if the dimensionality is too low. We thus enhance the RSM-based weak classifiers by extending RSM to multimodal-RSM. In tackling the elapsed time covariate, we use face information to enhance the RSM-based gait classifiers before the decision-level fusion. We find significant performance gain can be achieved when lower weight is assigned to the face information. We also employ a weak form of multimodal-RSM for gait recognition from low quality videos (with low resolution and low frame-rate) when other modalities are unavailable. In this case, model-based information is used to enhance the RSM-based weak classifiers. Then we point out the relationship of base classifier accuracy, classifier ensemble accuracy, and diversity among the base classifiers. By incorporating the model-based information (with lower weight) into the RSM-based weak classifiers, the diversity of the classifiers, which is positively correlated to the ensemble accuracy, can be enhanced. In contrast to multimodal systems, large intra-class variations may have a significant impact on unimodal systems. We model the effect of various unknown covariates as a partial feature corruption problem with unknown locations in the spatial domain. By making some assumptions in ideal cases analysis, we provide the theoretical basis of RSM-based classifier ensemble in the application of covariate-invariant gait recognition. However, in real cases, these assumptions may not hold precisely, and the performance may be affected when the intra-class variations are large. We propose a criterion to address this issue. That is, in the decision-level fusion stage, for a query gait with unknown covariates, we need to dynamically suppress the ratio of the false votes and the true votes before the majority voting. Two strategies are employed, i.e., local enhancing (LE) which can increase true votes, and the proposed hybrid decision-level fusion (HDF) which can decrease false votes. Based on this criterion, the proposed RSM-based HDF (RSM-HDF) framework achieves very competitive performance in tackling the covariates such as walking surface, clothing, and elapsed time, which were deemed as the open questions. The factor of camera viewpoint is different from other covariates. It alters the human appearance in a global manner. By employing unitary projection (UP), we form a new space, where the same subjects are closer from different views. However, it may also give rise to a large amount of feature distortions. We deem these distortions as the corrupted features with unknown locations in the new space (after UP), and use the RSM-HDF framework to address this issue. Robust view-invariant gait recognition can be achieved by using the UP-RSM-HDF framework. In this thesis, we propose a RSM-based classifier ensemble framework and its extensions to realise the covariate-invariant gait recognition. It is less sensitive to most of the covariate factors such as speed, shoe, carrying condition, walking surface, video quality, clothing, elapsed time, camera viewpoint, etc., and it outperforms other state-of-the-art algorithms significantly on all the major public gait databases. Specifically, our method can achieve very competitive performance against (large changes in) view, clothing, walking surface, elapsed time, etc., which were deemed as the most difficult covariate factors.
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Jhinaoui, Ahmed. "Subspace-based identification and vibration monitoring algorithms for rotating systems." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S161.
Full textAbstract:
Les méthodes d'identification dites sous-espace sont largement utilisées pour la caractérisation des modes propres et la surveillance des structures mécaniques. Elles ont fait leurs preuves pour les systèmes dont la dynamique est invariante dans le temps. Elles ne sont, toutefois, pas adaptées à des systèmes à rotors comme les hélicoptères et les éoliennes qui, de part leurs parties tournantes, sont périodiques dans le temps. Le but de cette thèse est d'étendre le champ d'application de ces méthodes à cette classe particulière de systèmes. Tout d'abord, un algorithme qui permet d'identifier certaine structure modale, dite de Floquet, est proposée. Ensuite, une étude de sensibilité est réalisée dans le but de quantifier les incertitudes, liées aux bruits ou à d'autres facteurs, sur les paramètres modaux identifiés. Enfin et partant de l'algorithme d'identification, une méthode de détection d'instabilité est développée. Cette méthode est basée sur la définition d'un résidu, fonction des paramètres modaux, et la surveillance d'un changement éventuel de ce résidu qui correspond à une déviation vers un régime instable. Ces méthodes ont été appliquées à des modèles numériques et à des données expérimentalesSubspace identification methods are widely used for caracterizing modal param-eters and for vibration monitoring of mechanical structures. They were shown powerful for the so-called linear time-invariant systems. However, they are not adapted to rotating sys-tems such as helicopters and wind turbines, which are inherently time-periodic systems. The goal of this thesis is to extend the applicability of these methods to this particular class of systems. First, a new identification algorithm is suggested. This algorithm permits to iden-tify the so-called Floquet modal structure. Then, a sensitivity study is conducted in order to quantify uncertainties, related to noises and other sources, about the identified modal param-eters. Finally and based on the suggested identification algorithm, a method for instability detection is developed. The main feature of this method is to define some residual, which is function of modal parameters, then to detect an eventual change over it which means a possible deviation toward an unstable regime. The suggested methods were applied to both numerical and experimental data
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Benner, P., V. Mehrmann, and H. Xu. "A new method for computing the stable invariant subspace of a real Hamiltonian matrix or Breaking Van Loans curse?" Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801309.
Full textAbstract:
A new backward stable, structure preserving method of complexity
O(n^3) is presented for computing the stable invariant subspace of
a real Hamiltonian matrix and the stabilizing solution of the
continuous-time algebraic Riccati equation. The new method is based
on the relationship between the invariant subspaces of the
Hamiltonian matrix H and the extended matrix /0 H\ and makes use
\H 0/
of the symplectic URV-like decomposition that was recently
introduced by the authors.
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Maree, J. P. (Johannes Philippus). "Fault detection for the Benfield process using a closed-loop subspace re-identification approach." Diss., University of Pretoria, 2008. http://hdl.handle.net/2263/29844.
Full textAbstract:
Closed-loop system identification and fault detection and isolation are the two fundamental building blocks of process monitoring. Efficient and accurate process monitoring increases plant availability and utilisation. This dissertation investigates a subspace system identification and fault detection methodology for the Benfield process, used by Sasol, Synfuels in Secunda, South Africa, to remove CO2 from CO2-rich tail gas. Subspace identification methods originated between system theory, geometry and numerical linear algebra which makes it a computationally efficient tool to estimate system parameters. Subspace identification methods are classified as Black-Box identification techniques, where it does not rely on a-priori process information and estimates the process model structure and order automatically. Typical subspace identification algorithms use non-parsimonious model formulation, with extra terms in the model that appear to be non-causal (stochastic noise components). These extra terms are included to conveniently perform subspace projection, but are the cause for inflated variance in the estimates, and partially responsible for the loss of closed-loop identifiably. The subspace identification methodology proposed in this dissertation incorporates two successive LQ decompositions to remove stochastic components and obtain state-space models of the plant respectively. The stability of the identified plant is further guaranteed by using the shift invariant property of the extended observability matrix by appending the shifted extended observability matrix by a block of zeros. It is shown that the spectral radius of the identified system matrices all lies within a unit boundary, when the system matrices are derived from the newly appended extended observability matrix. The proposed subspace identification methodology is validated and verified by re-identifying the Benfield process operating in closed-loop, with an RMPCT controller, using measured closed-loop process data. Models that have been identified from data measured from the Benfield process operating in closed-loop with an RMPCT controller produced validation data fits of 65% and higher. From residual analysis results, it was concluded that the proposed subspace identification method produce models that are accurate in predicting future outputs and represent a wide variety of process inputs. A parametric fault detection methodology is proposed that monitors the estimated system parameters as identified from the subspace identification methodology. The fault detection methodology is based on the monitoring of parameter discrepancies, where sporadic parameter deviations will be detected as faults. Extended Kalman filter theory is implemented to estimate system parameters, instead of system states, as new process data becomes readily available. The extended Kalman filter needs accurate initial parameter estimates and is thus periodically updated by the subspace identification methodology, as a new set of more accurate parameters have been identified. The proposed fault detection methodology is validated and verified by monitoring process behaviour of the Benfield process. Faults that were monitored for, and detected include foaming, flooding and sensor faults. Initial process parameters as identified from the subspace method can be tracked efficiently by using an extended Kalman filter. This enables the fault detection methodology to identify process parameter deviations, with a process parameter deviation sensitivity of 2% or higher. This means that a 2% parameter deviation will be detected which greatly enhances the fault detection efficiency and sensitivity.Dissertation (MEng)--University of Pretoria, 2008.
Electrical, Electronic and Computer Engineering
unrestricted
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Rubensson, Emanuel H. "Matrix Algebra for Quantum Chemistry." Doctoral thesis, Stockholm : Bioteknologi, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9447.
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Hovelaque, Vincent. "Analyse structurelle, géométrique et graphique des systèmes linéaires structurés." Grenoble INPG, 1997. http://www.theses.fr/1997INPG0137.
Full textAbstract:
Les systemes lineaires structures sont decrits par une representation d'etat de la forme (a,b,c) ou les elements des matrices a, b et c sont supposes soit nuls soit des parametres libres. Pour de tels systemes, on etudie des proprietes structurelles (ou generiques), i. E. Des proprietes vraies pour presque tout ensemble de parametres. A un systeme structure, on associe un graphe oriente qui contient l'information structurelle du systeme. Les contributions de cette these s'inscrivent dans trois domaines : geometrique, structurel et algorithmique. En theorie geometrique, la caracterisation de sous-espaces fixes particuliers a permis de resoudre le probleme de rejet de perturbation par retour de sortie dans le cas des systemes structures. D'un point de vue structurel, il est montre que les differents types de zeros generiques sont tous en 0 et peuvent etre directement caracterises sur le graphe associe. Cette approche structurelle a permis de determiner les dimensions generiques des blocs de la decomposition de kalman. D'autre part, une etude de l'algorithme primal-dual de recherche d'un flot maximum de cout minimum a permis de developper une methode efficace de calcul de la structure a l'infini generique. Differents resultats de cette these sont illustres sur un modele de colonne a distiller.
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Deeley, Robin. "Orbit operator and invariant subspaces." Thesis, 2006. http://hdl.handle.net/1828/2089.
Full textAbstract:
The invariant subspace problem is the long-standing question whether every operator on a Hilbert space of dimension greater than one has a non-trivial invariant subspace. Although the problem is unsolved in the Hilbert space case, there are counter-examples for operators acting on certain well-known non-reflexive Banach spaces. These counter-examples are constructed by considering a single orbit and then extending continuously to a hounded linear map on the entire space. Based on this process, we introduce an operator which has properties closely linked with an orbit. We call this operator the orbit operator.
In the first part of the thesis, examples and basic properties of the orbit operator are discussed. Next, properties linking invariant subspaces to properties of the orbit operator are presented. Topics include the kernel and range of the orbit operator, compact operators, dilation theory, and Rotas theorem. Finally, we extend results obtained for strict contractions to contractions.
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Popov, Alexey. "Invariant subspaces of certain classes of operators." Phd thesis, 2011. http://hdl.handle.net/10048/1906.
Full textAbstract:
The first part of the thesis studies invariant subspaces of strictly singular operators. By a celebrated result of Aronszajn and Smith, every compact operator has an invariant subspace. There are two classes of operators which are close to compact operators: strictly singular and finitely strictly singular operators. Pelczynski asked whether every strictly singular operator has an invariant subspace. This question was answered by Read in the negative. We answer the same question for finitely strictly singular operators, also in the negative. We also study Schreier singular operators. We show that this subclass of strictly singular operators is closed under multiplication by bounded operators. In addition, we find some sufficient conditions for a product of Schreier singular operators to be compact.
The second part studies almost invariant subspaces. A subspace Y of a Banach space is almost invariant under an operator T if TY is a subspace of Y+F for some finite-dimensional subspace F ("error"). Almost invariant subspaces of weighted shift operators are investigated. We also study almost invariant subspaces of algebras of operators. We establish that if an algebra is norm closed then the dimensions of "errors" for the operators in the algebra are uniformly bounded. We obtain that under certain conditions, if an algebra of operators has an almost invariant subspace then it also has an invariant subspace. Also, we study the question of whether an algebra and its closure have the same almost invariant subspaces.
The last two parts study collections of positive operators (including positive matrices) and their invariant subspaces. A version of Lomonosov theorem about dual algebras is obtained for collections of positive operators. Properties of indecomposable (i.e., having no common invariant order ideals) semigroups of nonnegative matrices are studied. It is shown that the "smallness" (in various senses) of some entries of matrices in an indecomposable semigroup of positive matrices implies the "smallness" of the entire semigroup.Mathematics
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Yu, Ping Chang, and 游品章. "Computation of Stable Invariant Subspaces of Symplectic Pencils." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/47657042543363483658.
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Kleper, Dvir. "Invariant subspaces of composition operators on weighted Hardy-Hilbert spaces /." 2008. http://proquest.umi.com/pqdlink?did=1659892511&sid=4&Fmt=2&clientId=12520&RQT=309&VName=PQD.
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Bošek, Jaroslav [Verfasser]. "Continuation of invariant subspaces in bifurcation problems / vorgelegt von Jaroslav Bošek." 2003. http://d-nb.info/972781196/34.
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Trumpf, Jochen. "On the geometry and parametrization of almost invariant subspaces and observer theory." Doctoral thesis, 2002. https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-5034.
Full textAbstract:
In my Ph.D. thesis "On the geometry and parametrization of almost invariant subspaces and observer theory" I consider the set of almost conditioned invariant subspaces of fixed dimension for a given fixed linear finite-dimensional time-invariant observable control system in state space form. Almost conditioned invariant subspaces were introduced by Willems. They generalize the concept of a conditioned invariant subspace requiring the invariance condition to hold only up to an arbitrarily small deviation in the metric of the state space. One of the goals of the theory of almost conditioned invariant subspaces was to identify the subspaces appearing as limits of sequences of conditioned invariant subspaces. An example due to {\"O}zveren, Verghese and Willsky, however, shows that the set of almost conditioned invariant subspaces is not big enough. I address this question in a joint paper with Helmke and Fuhrmann (Towards a compactification of the set of conditioned invariant subspaces, Systems and Control Letters, 48(2):101-111, 2003). Antoulas derived a description of conditioned invariant subspaces as kernels of permuted and truncated reachability matrices of controllable pairs of the appropriate size. This description was used by Helmke and Fuhrmann to construct a diffeomorphism from the set of similarity classes of certain controllable pairs onto the set of tight conditioned invariant subspaces. In my thesis I generalize this result to almost conditioned invariant subspaces describing them in terms of restricted system equivalence classes of controllable triples. Furthermore, I identify the controllable pairs appearing in the kernel representations of conditioned invariant subspaces as being induced by corestrictions of the original system to the subspace. Conditioned invariant subspaces are known to be closely related to partial observers. In fact, a tracking observer for a linear function of the state of the observed system exists if and only if the kernel of that function is conditioned invariant. In my thesis I show that the system matrices of the observers are in fact the corestrictions of the observed system to the kernels of the observed functions. They in turn are closely related to partial realizations. Exploring this connection further, I prove that the set of tracking observer parameters of fixed size, i.e. tracking observers of fixed order together with the functions they are tracking, is a smooth manifold. Furthermore, I construct a vector bundle structure for the set of conditioned invariant subspaces of fixed dimension together with their friends, i.e. the output injections making the subspaces invariant, over that manifold. Willems and Trentelman generalized the concept of a tracking observer by including derivatives of the output of the observed system in the observer equations (PID-observers). They showed that a PID-observer for a linear function of the state of the observed system exists if and only if the kernel of that function is almost conditioned invariant. In my thesis I replace PID-observers by singular systems, which has the advantage that the system matrices of the observers coincide with the matrices appearing in the kernel representations of the subspaces. In a second approach to the parametrization of conditioned invariant subspaces Hinrichsen, M{\"u}nzner and Pr{\"a}tzel-Wolters, Fuhrmann and Helmke and Ferrer, F. Puerta, X. Puerta and Zaballa derived a description of conditioned invariant subspaces in terms of images of block Toeplitz type matrices. They used this description to construct a stratification of the set of conditioned invariant subspaces of fixed dimension into smooth manifolds. These so called Brunovsky strata consist of all the subspaces with fixed restriction indices. They constructed a cell decomposition of the Brunovsky strata into so called Kronecker cells. In my thesis I show that in the tight case this cell decomposition is induced by a Bruhat decomposition of a generalized flag manifold. I identify the adherence order of the cell decomposition as being induced by the reverse Bruhat orderIn meiner Doktorarbeit "On the geometry and parametrization of almost invariant subspaces and observer theory" betrachte ich die Menge der fast (C,A)-invarianten Unterräume fester Dimension zu einem vorgegebenen linearen endlichdimensionalen zeitinvarianten beobachtbaren Kontrollsystem in Zustandsraumdarstellung. Der Begriff der fast (C,A)-invarianten Unterräume geht auf Willems zurück. Er verallgemeinert das Konzept eines (C,A)-invarianten Unterraums dahingehend, daß die Invarianzeigenschaft nur bis auf eine beliebig kleine Abweichung in der Metrik des Zustandsraumes erfüllt sein muß. Eines der Ziele der Theorie der fast (C,A)-invarianten Unterräume war es, diejenigen Unterräume zu charakterisieren, die als Grenzwerte von Folgen (C,A)-invarianter Unterräume auftreten. Özveren, Verghese und Willsky haben jedoch ein Beispiel angegeben, das zeigt, daß die Menge der fast (C,A)-invarianten Unterräume hierfür nicht groß genug ist. Auf diese Problematik gehe ich in einer gemeinsamen Arbeit mit U. Helmke und P.A. Fuhrmann (Towards a compactification of the set of conditioned invariant subspaces, Systems and Control Letters, 48(2):101-111, 2003) ein, die nicht Teil meiner Dissertation ist. Antoulas hat eine Beschreibung von (C,A)-invarianten Unterräumen als Kerne von permutierten und abgeschnittenen Erreichbarkeitsmatrizen geeigneter Größe angegeben. Diese Beschreibung benutzen Fuhrmann und Helmke um einen Diffeomorphismus von der Menge der Ähnlichkeitsklassen bestimmter kontrollierbarer Matrizenpaare auf die Menge der "tight" (C,A)-invarianten Unterräume zu konstruieren. In meiner Dissertation verallgemeinere ich dieses Resultat auf fast (C,A)-invariante Unterräume, indem ich sie mit Hilfe von "restricted system equivalence"-Klassen kontrollierbarer Matrizentripel darstelle. Darüberhinaus identifiziere ich die kontrollierbaren Matrizenpaare, die in der Kerndarstellung (C,A)-invarianter Unterräume auftreten, als Korestriktionen des ursprünglichen Systems auf den jeweiligen Unterraum. Es besteht eine enge Verbindung zwischen (C,A)-invarianten Unterräumen und partiellen Beobachtern. In der Tat existiert ein "tracking" Beobachter für eine lineare Funktion des Zustandes des beobachteten Systems genau dann, wenn der Kern dieser Funktion (C,A)-invariant ist. In meiner Dissertation zeige ich, daß die Systemmatrizen der Beobachter mit den Korestriktionen des beobachteten Systems auf die Kerne der beobachteten Funktionen übereinstimmen. Diese wiederum stehen in enger Beziehung zu partiellen Realisierungen. Weiter beweise ich, daß die Menge der "tracking" Beobachter-Parameter fester Größe, das heißt der "tracking" Beobachter fester Ordnung zusammen mit den beobachteten Funktionen, eine glatte Mannigfaltigkeitsstruktur trägt. Ich konstruiere eine Vektorbündelstruktur auf der Menge der (C,A)-invarianten Unterräume fester Dimension zusammen mit ihren "Freunden", das heißt den "output injections", welche den jeweiligen Unterraum invariant machen, wobei die Beobachtermannigfaltigkeit als Basisraum dient. Willems und Trentelman haben das Konzept eines "tracking" Beobachter verallgemeinert, indem sie auch Ableitungen des Ausgangs des beobachteten Systems in die Beobachtergleichungen aufnahmen (PID-Beobachter). Sie haben gezeigt, daß ein PID-Beobachter für eine lineare Funktion des Zustands des beobachteten Systems genau dann existiert, wenn der Kern dieser Funktion fast (C,A)-invariant ist. In meiner Dissertation ersetze ich die PID-Beobachter durch singuläre Systeme, was den Vorteil hat, daß die Systemmatrizen des Beobachters mit den Matrizen übereinstimmen, die in der Kerndarstellung des Unterraums auftauchen. (C,A)-invariante Unterräume lassen sich auch als Bildräume von Block-Toeplitz-Matrizen beschreiben. Hinrichsen, Münzner und Prätzel-Wolters, Fuhrmann und Helmke, und Ferrer, F. Puerta, X. Puerta und Zaballa benutzen diesen Zugang, um eine Stratifizierung der Menge der (C,A)-invarianten Unterräume fester Dimension in glatte Mannigfaltigkeiten zu konstruieren. Diese sogenannten Brunovsky-Strata bestehen aus all den Unterräumen, für die die Einschränkung des Systems auf den Unterraum jeweils vorgegebene Beobachtbarkeitsindizes hat. Obige Autoren konstruieren auch eine Zellzerlegung der Brunovsky-Strata in sogenannte Kronecker-Zellen. In meiner Dissertation zeige ich, daß im "tight" Fall diese Zellzerlegung von einer Bruhat-Zerlegung einer verallgemeinerten Fahnenmannigfaltigkeit induziert wird. Ich identifiziere die Adhärenzordnung der Zellzerlegung als inverse Bruhat-Ordnung
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Thompson, Derek Allen. "Restrictions to Invariant Subspaces of Composition Operators on the Hardy Space of the Disk." 2014. http://hdl.handle.net/1805/3881.
Full textAbstract:
Indiana University-Purdue University Indianapolis (IUPUI)Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as certain restrictions of the unilateral shift on the Hardy space of the disk. A composition operator with symbol fixing 0 has a nested sequence of invariant subspaces, and if the symbol is linear fractional and extremally noncompact, the restrictions to these subspaces all have the same norm and spectrum. Despite this evidence, we will use semigroup techniques to show many cases where the restrictions are still not unitarily equivalent.