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Academic literature on the topic 'Bounded linear operators'

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Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Bounded linear operators"

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Rashid, M. H. M. "Propertiesandfor Bounded Linear Operators." Journal of Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/848176.

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We shall consider properties which are related to Weyl type theorem for bounded linear operators , defined on a complex Banach space . These properties, that we callproperty, means that the set of all poles of the resolvent of of finite rank in the usual spectrum are exactly those points of the spectrum for which is an upper semi-Fredholm with index less than or equal to 0 and we callproperty, means that the set of all poles of the resolvent of in the usual spectrum are exactly those points of the spectrum for which is an upper semi--Fredholm with index less than or equal to 0. Properties and are related to a strong variants of classical Weyl’s theorem, the so-called property and property We shall characterize properties and in several ways and we shall also describe the relationships of it with the other variants of Weyl type theorems. Our main tool is localized version of the single valued extension property. Also, we consider the properties and in the frame of polaroid type operators.

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Bag, T., and S. K. Samanta. "Fuzzy bounded linear operators." Fuzzy Sets and Systems 151, no. 3 (May 2005): 513–47. http://dx.doi.org/10.1016/j.fss.2004.05.004.

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Ghosh, Puja, Debmalya Sain, and Kallol Paul. "Orthogonality of bounded linear operators." Linear Algebra and its Applications 500 (July 2016): 43–51. http://dx.doi.org/10.1016/j.laa.2016.03.009.

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Jasim, Muna, and Manal Ali. "Modules and Bounded Linear Operators." Journal of Al-Nahrain University-Science 19, no. 1 (March 2016): 168–72. http://dx.doi.org/10.22401/jnus.19.1.19.

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Bajryacharya, Prakash Muni, and Keshab Raj Phulara. "Extension of Bounded Linear Operators." Journal of Advanced College of Engineering and Management 2 (November 29, 2016): 11. http://dx.doi.org/10.3126/jacem.v2i0.16094.

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<p>In this article the problem entitled when does every member of a class of operators T : E → Y admit an extension operator T : X → Y in different approaches like injective spaces, separable injective spaces, the class of compact operators and extension Into C(K ) spaces has-been studied.</p><p><strong>Journal of Advanced College of Engineering and Management,</strong> Vol. 2, 2016, page: 11-13</p>

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Kudryashov, Yu L. "Dilatations of Linear Operators." Contemporary Mathematics. Fundamental Directions 66, no. 2 (December 15, 2020): 209–20. http://dx.doi.org/10.22363/2413-3639-2020-66-2-209-220.

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The article is devoted to building various dilatations of linear operators. The explicit construction of a unitary dilation of a compression operator is considered. Then the J -unitary dilatation of a bounded operator is constructed by means of the operator knot concept of a bounded linear operator. Using the Pavlov method, we construct the self-adjoint dilatation of a bounded dissipative operator. We consider spectral and translational representations of the self-adjoint dilatation of a densely defined dissipative operator with nonempty set of regular points. Using the concept of an operator knot for a bounded operator and the Cayley transform, we introduce an operator knot for a linear operator. By means of this concept, we construct the J -self-adjoint dilatation of a densely defined operator with a regular point. We obtain conditions of isomorphism of extraneous dilations and their minimality.

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Baskakov, A. G. "Linear differential operators with unbounded operator coefficients and semigroups of bounded operators." Mathematical Notes 59, no. 6 (June 1996): 586–93. http://dx.doi.org/10.1007/bf02307207.

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Bahreini, Manijeh, Elizabeth Bator, and Ioana Ghenciu. "Complemented Subspaces of Linear Bounded Operators." Canadian Mathematical Bulletin 55, no. 3 (September 1, 2012): 449–61. http://dx.doi.org/10.4153/cmb-2011-097-2.

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AbstractWe study the complementation of the space W(X, Y) of weakly compact operators, the space K(X, Y) of compact operators, the space U(X, Y) of unconditionally converging operators, and the space CC(X, Y) of completely continuous operators in the space L(X, Y) of bounded linear operators from X to Y. Feder proved that if X is infinite-dimensional and c0 ↪ Y, then K(X, Y) is uncomplemented in L(X, Y). Emmanuele and John showed that if c0 ↪ K(X, Y), then K(X, Y) is uncomplemented in L(X, Y). Bator and Lewis showed that if X is not a Grothendieck space and c0 ↪ Y, then W(X, Y) is uncomplemented in L(X, Y). In this paper, classical results of Kalton and separably determined operator ideals with property (∗) are used to obtain complementation results that yield these theorems as corollaries.

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Jung, W., R. Metzger, C. A. Morales, and H. Villavicencio. "A distance between bounded linear operators." Topology and its Applications 284 (October 2020): 107359. http://dx.doi.org/10.1016/j.topol.2020.107359.

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Xiao, Xiang-chun, Yu-can Zhu, Zhi-biao Shu, and Ming-ling Ding. "G-frames with bounded linear operators." Rocky Mountain Journal of Mathematics 45, no. 2 (April 2015): 675–93. http://dx.doi.org/10.1216/rmj-2015-45-2-675.

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Dissertations / Theses on the topic "Bounded linear operators"

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Turcu, George R. "Hypercyclic Extensions Of Bounded Linear Operators." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1386189984.

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Bahreini, Esfahani Manijeh. "Complemented Subspaces of Bounded Linear Operators." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4349/.

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For many years mathematicians have been interested in the problem of whether an operator ideal is complemented in the space of all bounded linear operators. In this dissertation the complementation of various classes of operators in the space of all bounded linear operators is considered. This paper begins with a preliminary discussion of linear bounded operators as well as operator ideals. Let L(X, Y ) be a Banach space of all bounded linear operator between Banach spaces X and Y , K(X, Y ) be the space of all compact operators, and W(X, Y ) be the space of all weakly compact operators. We denote space all operator ideals by O.

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O'Connor, B. J. "State diagrams for bounded and unbounded linear operators." Master's thesis, University of Cape Town, 1990. http://hdl.handle.net/11427/18245.

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Bibliography: pages 107-110.
The theme of this thesis is the construction of state diagrams and their implications. The author generalises most of the theorems in Chapter II of Goldberg [Gl] by dropping the assumption that the doin.ain of the operator is dense in X . The author also presents the standard Taylor-Halberg-Goldberg state diagrams [Gl, 61, 66]. Chapters II and III deal with F₊- and F₋-operators, which are generalisations of the ф₊- and ф₋-operators in Banach spaces of Gokhberg-Krein [GK]. Examples are given of F₊- and F₋-operators. Also, in Chapter III, the main theorems needed to construct the state diagrams of Chapter IV are discussed. The state diagrams of Chapter IV are based on states corresponding to F₊- and F₋-operators; in addition state diagrams relating T and T˝ under the assumptions ϒ(T) > 0 and ϒ(T΄) > 0 are derived. Second adjoints are important in Tauberian Theory (see Cross [Cl]). Chapters I and IV are the main chapters. In Chapter I of this thesis the author modifies many of the proofs appearing in Goldberg [Gl), to take account of the new definition of the adjoint.

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Abbott, Catherine Ann. "Operators on Continuous Function Spaces and Weak Precompactness." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331171/.

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If T:C(H,X)-->Y is a bounded linear operator then there exists a unique weakly regular finitely additive set function m:-->L(X,Y**) so that T(f) = ∫Hfdm. In this paper, bounded linear operators on C(H,X) are studied in terms the measure given by this representation theorem. The first chapter provides a brief history of representation theorems of these classes of operators. In the second chapter the represenation theorem used in the remainder of the paper is presented. If T is a weakly compact operator on C(H,X) with representing measure m, then m(A) is a weakly compact operator for every Borel set A. Furthermore, m is strongly bounded. Analogous statements may be made for many interesting classes of operators. In chapter III, two classes of operators, weakly precompact and QSP, are studied. Examples are provided to show that if T is weakly precompact (QSP) then m(A) need not be weakly precompact (QSP), for every Borel set A. In addition, it will be shown that weakly precompact and GSP operators need not have strongly bounded representing measures. Sufficient conditions are provided which guarantee that a weakly precompact (QSP) operator has weakly precompact (QSP) values. A sufficient condition for a weakly precomact operator to be strongly bounded is given. In chapter IV, weakly precompact subsets of L1(μ,X) are examined. For a Banach space X whose dual has the Radon-Nikodym property, it is shown that the weakly precompact subsets of L1(μ,X) are exactly the uniformly integrable subsets of L1(μ,X). Furthermore, it is shown that this characterization does not hold in Banach spaces X for which X* does not have the weak Radon-Nikodym property.

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Ghassel, Ali. "The radon split of radially acting linear integral operators on h¦2 with uniformly bounded double norms." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ48521.pdf.

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Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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Hernandez, Michelle Fernanda Pierri. "Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-19052009-161255/.

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Este trabalho está voltado para o estudo de uma classe de funções contínuas e limitadas f : [0; \'INFINITO\') \'SETA\' X para as quais existe \'omega\' \'> OU =\' 0 tal que \'lim IND. t\' \'SETA\' \'INFINITO\' (f(t + \'omega\') - f(t)) = 0. No decorrer do trabalho, chamaremos estas funções de S-assintoticamente \'omega\'-periódicas. Nós discutiremos propriedades qualitativas para estas funções e algumas relações entre este tipo de funções e a classe de funções assintoticamente \'omega\'-periódicas. Também estudaremos a existência de soluções fracas S-assintoticamente \'omega\'-periódicas para uma classe de primeira ordem de um problema de Cauchy abstrato bem como para algumas classes de equações diferenciais funcionais parciais neutras com retardo não limitado. Algumas aplicações para equações diferenciais parciais serão consideradas
This work is devoted to the study of the class of continuous and bounded functions f : [0 \'INFINIT\') \'ARROW\' X for which there exists \'omega\' > 0 such that \'limt IND.t \'ARROW\' \'INFINIT\'(f(t + \'omega\'!) - f(t)) = 0 (in the sequel called S-asymptotically !-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically \'omega\'-periodic functions. We also study the existence of S-asymptotically \'omega\'-periodic mild solutions for a first-order abstract Cauchy problem in Banach spaces and for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given

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Ugur, Omur. "Boundary Value Problems For Higher Order Linear Impulsive Differential Equations." Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/686691/index.pdf.

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_I The theory of impulsive di®
erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di®
erential equations. In this work, higher order linear impulsive equations at ¯
xed moments of impulses together with certain boundary conditions are investigated by making use of a Green'
s formula, constructed for piecewise di®
erentiable functions. Existence and uniqueness of solutions of such boundary value problems are also addressed. Properties of Green'
s functions for higher order impulsive boundary value prob- lems are introduced, showing a striking di®
erence when compared to classical bound- ary value problems of ordinary di®
erential equations. Necessarily, instead of an or- dinary Green'
s function there corresponds a sequence of Green'
s functions due to impulses. Finally, as a by-product of boundary value problems, eigenvalue problems for higher order linear impulsive di®
erential equations are studied. The conditions for the existence of eigenvalues of linear impulsive operators are presented. Basic properties of eigensolutions of self-adjoint operators are also investigated. In particular, a necessary and su±
cient condition for the self-adjointness of Sturm-Liouville opera- tors is given. The corresponding integral equations for boundary value and eigenvalue problems are also demonstrated in the present work.

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Mkadem, Mohamed Amine. "Flow-shop with time delays, linear modeling and exact solution approaches." Thesis, Compiègne, 2017. http://www.theses.fr/2017COMP2390/document.

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Dans le cadre de cette thèse, nous traitons le problème de flow-shop à deux machines avec temps de transport où l’objectif consiste à minimiser le temps de complétion maximal. Dans un premier temps, nous nous sommes intéressés à la modélisation de ce problème. Nous avons proposé plusieurs programmes linéaires en nombres entiers. En particulier, nous avons introduit une formulation linéaire basée sur une généralisation non triviale du modèle d’affectation pour le cas où les durées des opérations sur une même machine sont identiques. Dans un deuxième temps, nous avons élargi la portée de ces formulations mathématiques pour développer plusieurs bornes inférieures et un algorithme exact basé sur la méthode de coupe et branchement (Branch-and-Cut). En effet, un ensemble d’inégalités valides a été considéré afin d’améliorer la relaxation linéaire de ces programmes et d’accélérer leur convergence. Ces inégalités sont basées sur la proposition de nouvelles règles de dominance et l’identification de sous-instances faciles à résoudre. L’identification de ces sous-instances revient à déterminer les cliques maximales dans un graphe d’intervalles. En plus des inégalités valides, la méthode exacte proposée inclut la considération d’une méthode heuristique et d’une procédure visant à élaguer les nœuds. Enfin, nous avons proposé un algorithme par séparation et évaluation (Branch-and-Bound) pour lequel, nous avons introduit des règles de dominance et une méthode heuristique basée sur la recherche locale. Nos expérimentations montrent l’efficacité de nos approches qui dominent celles de la littérature. Ces expérimentations ont été conduites sur plusieurs classes d’instances qui incluent celles de la littérature, ainsi que des nouvelles classes d’instances où les algorithmes de la littérature se sont montrés peu efficaces
In this thesis, we study the two-machine flow-shop problem with time delays in order to minimize the makespan. First, we propose a set of Mixed Integer Programming (MIP) formulations for the problem. In particular, we introduce a new compact mathematical formulation for the case where operations are identical per machine. The proposed mathematical formulations are then used to develop lower bounds and a branch-and-cut method. A set of valid inequalities is proposed in order to improve the linear relaxation of the MIPs. These inequalities are based on proposing new dominance rules and computing optimal solutions of polynomial-time-solvable sub-instances. These sub-instances are extracted by computing all maximal cliques on a particular Interval graph. In addition to the valid inequalities, the branch-and-cut method includes the consideration of a heuristic method and a node pruning procedure. Finally, we propose a branch-and-bound method. For which, we introduce a local search-based heuristic and dominance rules. Experiments were conducted on a variety of classes of instances including both literature and new proposed ones. These experiments show the efficiency of our approaches that outperform the leading methods published in the research literature

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Neamatian, Monemi Rahimeh. "Fixed cardinality linear ordering problem, polyhedral studies and solution methods." Thesis, Clermont-Ferrand 2, 2014. http://www.theses.fr/2014CLF22516/document.

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Le problème d’ordre linéaire (LOP) a reçu beaucoup d’attention dans différents domaines d’application, allant de l’archéologie à l’ordonnancement en passant par l’économie et même de la psychologie mathématique. Ce problème est aussi connu pour être parmi les problèmes NP-difficiles. Nous considérons dans cette thèse une variante de (LOP) sous contrainte de cardinalité. Nous cherchons donc un ordre linéaire d’un sous-ensemble de sommets du graphe de préférences de cardinalité fixée et de poids maximum. Ce problème, appelé (FCLOP) pour ’fixed-cardinality linear ordering problem’, n’a pas été étudié en tant que tel dans la littérature scientifique même si plusieurs applications dans les domaines de macro-économie, de classification dominante ou de transport maritime existent concrètement. On retrouve en fait ses caractéristiques dans les modèles étendus de sous-graphes acycliques. Le problème d’ordre linéaire est déjà connu comme un problème NP-difficile et il a donné lieu à de nombreuses études, tant théoriques sur la structure polyédrale de l’ensemble des solutions réalisables en variables 0-1 que numériques grâce à des techniques de relaxation et de séparation progressive. Cependant on voit qu’il existe de nombreux cas dans la littérature, dans lesquelles des solveurs de Programmation Linéaire en nombres entiers comme CPLEX peuvent en résoudre certaines instances en moins de 10 secondes, mais une fois que la cardinalité est limitée, ces mêmes instances deviennent très difficiles à résoudre. Sur les aspects polyédraux, nous avons étudié le polytope de FCLOP, défini plusieurs classes d’inégalités valides et identifié la dimension ainsi que certaines inégalités qui définissent des facettes pour le polytope de FCLOP. Nous avons introduit un algorithme Relax-and-Cut basé sur ces résultats pour résoudre les instances du problème. Dans cette étude, nous nous sommes également concentrés sur la relaxation Lagrangienne pour résoudre ces cas difficiles. Nous avons étudié différentes stratégies de relaxation et nous avons comparé les bornes duales par rapport à la consolidation obtenue à partir de chaque stratégie de relâcher les contraintes afin de détecter le sous-ensemble des contraintes le plus approprié. Les résultats numériques montrent que nous pouvons trouver des bornes duales de très haute qualité. Nous avons également mis en place une méthode de décomposition Lagrangienne. Dans ce but, nous avons décomposé le modèle de FCLOP en trois sous-problèmes (au lieu de seulement deux) associés aux contraintes de ’tournoi’, de ’graphes sans circuits’ et de ’cardinalité’. Les résultats numériques montrent une amélioration significative de la qualité des bornes duales pour plusieurs cas. Nous avons aussi mis en oeuvre une méthode de plans sécants (cutting plane algorithm) basée sur la relaxation pure des contraintes de circuits. Dans cette méthode, on a relâché une partie des contraintes et on les a ajoutées au modèle au cas où il y a des de/des violations. Les résultats numériques montrent des performances prometteuses quant à la réduction du temps de calcul et à la résolution d’instances difficiles hors d’atteinte des solveurs classiques en PLNE
Linear Ordering Problem (LOP) has receive significant attention in different areas of application, ranging from transportation and scheduling to economics and even archeology and mathematical psychology. It is classified as a NP-hard problem. Assume a complete weighted directed graph on V n , |V n |= n. A permutation of the elements of this finite set of vertices is a linear order. Now let p be a given fixed integer number, 0 ≤ p ≤ n. The p-Fixed Cardinality Linear Ordering Problem (FCLOP) is looking for a subset of vertices containing p nodes and a linear order on the nodes in S. Graphically, there exists exactly one directed arc between every pair of vertices in an LOP feasible solution, which is also a complete cycle-free digraph and the objective is to maximize the sum of the weights of all the arcs in a feasible solution. In the FCLOP, we are looking for a subset S ⊆ V n such that |S|= p and an LOP on these S nodes. Hence the objective is to find the best subset of the nodes and an LOP over these p nodes that maximize the sum of the weights of all the arcs in the solution. Graphically, a feasible solution of the FCLOP is a complete cycle-free digraph on S plus a set of n − p vertices that are not connected to any of the other vertices. There are several studies available in the literature focused on polyhedral aspects of the linear ordering problem as well as various exact and heuristic solution methods. The fixed cardinality linear ordering problem is presented for the first time in this PhD study, so as far as we know, there is no other study in the literature that has studied this problem. The linear ordering problem is already known as a NP-hard problem. However one sees that there exist many instances in the literature that can be solved by CPLEX in less than 10 seconds (when p = n), but once the cardinality number is limited to p (p < n), the instance is not anymore solvable due to the memory issue. We have studied the polytope corresponding to the FCLOP for different cardinality values. We have identified dimension of the polytope, proposed several classes of valid inequalities and showed that among these sets of valid inequalities, some of them are defining facets for the FCLOP polytope for different cardinality values. We have then introduced a Relax-and-Cut algorithm based on these results to solve instances of the FCLOP. To solve the instances of the problem, in the beginning, we have applied the Lagrangian relaxation algorithm. We have studied different relaxation strategies and compared the dual bound obtained from each case to detect the most suitable subproblem. Numerical results show that some of the relaxation strategies result better dual bound and some other contribute more in reducing the computational time and provide a relatively good dual bound in a shorter time. We have also implemented a Lagrangian decomposition algorithm, decom-6 posing the FCLOP model to three subproblems (instead of only two subproblems). The interest of decomposing the FCLOP model to three subproblems comes mostly from the nature of the three subproblems, which are relatively quite easier to solve compared to the initial FCLOP model. Numerical results show a significant improvement in the quality of dual bounds for several instances. We could also obtain relatively quite better dual bounds in a shorter time comparing to the other relaxation strategies. We have proposed a cutting plane algorithm based on the pure relaxation strategy. In this algorithm, we firstly relax a subset of constraints that due to the problem structure, a very few number of them are active. Then in the course of the branch-and-bound tree we verify if there exist any violated constraint among the relaxed constraints or. Then the characterized violated constraints will be globally added to the model. (...)

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Books on the topic "Bounded linear operators"

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Kubrusly, Carlos S. Spectral Theory of Bounded Linear Operators. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-33149-8.

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Harte, Robin. Invertibility and singularity for bounded linear operators. New York: M. Dekker, 1988.

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1941-, Șabac Mihai, ed. Lie algebras of bounded operators. Basel: Birkhäuser Verlag, 2001.

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Dragomir, Silvestru Sever. Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17459-0.

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Pisier, Gilles. Similarity problems and completely bounded maps. 2nd ed. Berlin: Springer, 2001.

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Similarity problems and completely bounded maps. Berlin: Springer, 1996.

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Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

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1975-, Sims Robert, and Ueltschi Daniel 1969-, eds. Entropy and the quantum II: Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Providence, R.I: American Mathematical Society, 2011.

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Kubrusly, Carlos S. Spectral Theory of Bounded Linear Operators. Birkhäuser, 2020.

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Invertibility and Singularity for Bounded Linear Operators. Dover Publications, Incorporated, 2016.

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Book chapters on the topic "Bounded linear operators"

1

Blanchard, Philippe, and Erwin Brüning. "Bounded Linear Operators." In Mathematical Methods in Physics, 275–91. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0049-9_21.

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Wong, M. W. "Bounded Linear Operators." In Discrete Fourier Analysis, 107–12. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0116-4_15.

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Zhu, Kehe. "Bounded linear operators." In Mathematical Surveys and Monographs, 1–32. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/138/01.

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Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis. "Bounded linear operators." In Graduate Studies in Mathematics, 55–73. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/066/04.

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Blanchard, Philippe, and Erwin Brüning. "Bounded Linear Operators." In Mathematical Methods in Physics, 307–23. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14045-2_22.

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Kress, Rainer. "Bounded and Compact Operators." In Linear Integral Equations, 17–32. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9593-2_2.

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Kress, Rainer. "Bounded and Compact Operators." In Linear Integral Equations, 13–24. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4_2.

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Kress, Rainer. "Bounded and Compact Operators." In Linear Integral Equations, 15–27. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_2.

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Edmunds, David E., and W. Desmond Evans. "Representation of Bounded Linear Operators." In Representations of Linear Operators Between Banach Spaces, 127–40. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0642-8_3.

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Bezandry, Paul H., and Toka Diagana. "Bounded and Unbounded Linear Operators." In Almost Periodic Stochastic Processes, 21–59. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9476-9_2.

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Conference papers on the topic "Bounded linear operators"

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Aiena, Pietro. "Weyl type theorems for bounded linear operators on Banach spaces." In Proceedings of the Fourth International School — In Memory of Professor Antonio Aizpuru Tomás. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814335812_0002.

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Balas, Mark J., and Susan A. Frost. "Adaptive Tracking Control for Linear Infinite Dimensional Systems." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9098.

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Tracking an ensemble of basic signals is often required of control systems in general. Here we are given a linear continuous-time infinite-dimensional plant on a Hilbert space and a space of tracking signals generated by a finite basis, and we show that there exists a stabilizing direct adaptive control law that will stabilize the plant and cause it to asymptotically track any member of this collection of signals. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. There is no state or parameter estimation used in this adaptive approach. Our results are illustrated by adaptive control of general linear diffusion systems.

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Della Monica, Dario, Nicola Gigante, Angelo Montanari, Pietro Sala, and Guido Sciavicco. "Bounded Timed Propositional Temporal Logic with Past Captures Timeline-based Planning with Bounded Constraints." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/140.

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Within the timeline-based framework, planning problems are modeled as sets of independent, but interacting, components whose behavior over time is described by a set of temporal constraints. Timeline-based planning is being used successfully in a number of complex tasks, but its theoretical properties are not so well studied. In particular, while it is known that Linear Temporal Logic (LTL) can capture classical action-based planning, a similar logical characterization was not available for timeline-based planning formalisms. This paper shows that timeline-based planning with bounded temporal constraints can be captured by a bounded version of Timed Propositional Temporal Logic, augmented with past operators, which is an extension of LTL originally designed for the verification of real-time systems. As a byproduct, we get that the proposed logic is expressive enough to capture temporal action-based planning problems.

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Balas, Mark J. "Augmentation of Fixed Gain Controlled Infinite Dimensional Systems With Direct Adaptive Control." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23179.

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Abstract Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. We augment this controller with a direct adaptive controller that will maintain stability of the full closed loop system even when the fixed gain controller fails to do so. We prove that the transmission zeros of the combined system are the original open loop transmission zeros, and the point spectrum of the controller alone. Therefore, the combined plant plus controller is Almost Strictly Dissipative (ASD) if and only if the original open loop system is minimum phase, and the fixed gain controller alone is exponentially stable. This result is true whether the fixed gain controller is finite or infinite dimensional. In particular this guarantees that a controller for an infinite dimensional plant based on a reduced -order approximation can be stabilized by augmentation with direct adaptive control to mitigate risks. These results are illustrated by application to direct adaptive control of general linear diffusion systems on a Hilbert space that are described by self-adjoint operators with compact resolvent.

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Balas, Mark J., and Susan A. Frost. "A Stabilization of Fixed Gain Controlled Infinite Dimensional Systems by Augmentation With Direct Adaptive Control." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3726.

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Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.

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Akgül, A., and M. Giyas Sakar. "Reproducing kernel functions and bounded linear operator for solving fractional nonlinear boundary value problems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044174.

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Liu, Chenchen, and Wai Ho Mow. "Bounds on the expected rank of sparse linear operator channel matrices." In 2013 19th Asia-Pacific Conference on Communications (APCC). IEEE, 2013. http://dx.doi.org/10.1109/apcc.2013.6766002.

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Fijalkow, Nathanaël, Bastien Maubert, Aniello Murano, and Moshe Vardi. "Assume-Guarantee Synthesis for Prompt Linear Temporal Logic." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/17.

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Prompt-LTL extends Linear Temporal Logic with a bounded version of the ``eventually'' operator to express temporal requirements such as bounding waiting times. We study assume-guarantee synthesis for prompt-LTL: the goal is to construct a system such that for all environments satisfying a first prompt-LTL formula (the assumption) the system composed with this environment satisfies a second prompt-LTL formula (the guarantee). This problem has been open for a decade. We construct an algorithm for solving it and show that, like classical LTL synthesis, it is 2-EXPTIME-complete.

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Lee, Jaecheol, Shahin Tasoujian, Karolos Grigoriadis, and Matthew Franchek. "Output-Feedback Linear Parameter Varying Control of Permanent Magnet Synchronous Motors." In ASME 2020 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/dscc2020-3331.

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Abstract This paper investigates the design of an output feedback linear parameter-varying (LPV) gain-scheduled controller for the speed regulation of a surface permanent magnet synchronous motor (SPMSM). Motor dynamics is defined in the stationary reference (α – β) frame and a parameter-varying model formulation is provided to describe the SPMSM nonlinear dynamics. In this context, a robust gain-scheduled LPV output-feedback dynamic controller is designed to satisfy the asymptotic stability of the closed-loop system and meet desired performance requirements, and guarantee robustness against norm-bounded uncertainties and disturbances. The real-time impact of temperature variation on the winding resistance and magnet flux during motor operations are considered in the LPV modelling and the subsequent control design to address demagnetization effects in the motor response. The controller synthesis conditions are formulated in a convex linear matrix inequality (LMI) constraint framework. Finally, the validity of the proposed control strategy is assessed in simulation studies, and the results are compared to the results of the conventional field-oriented control (FOC) method. The results of the simulation demonstrate that the proposed controller provides improved transient response with respect to settling time, overshoot, and disturbance rejection in tracking the velocity profile under the influence of parameter and temperature variations and disturbances.

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Joneja, Ajay, Angela Tam, and Fu Jing. "Draping 2D Patterns Onto 3D Surfaces." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dfm-48170.

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We describe a simple new CAD operator that allows draping of given 2D patterns onto the surface of a 3D mold. The 2D pattern is any closed, connected polygon or a polygonal approximation of a shape bounded by curves. The mold is typically described in terms of any standard surface representation scheme, such as NURBS or B-Splines. The draping is achieved by mapping skeletal lines on the 2D pattern onto corresponding geodesic curves on the 3D surface. If the mold surface is developable, our method gives a draping with zero distortion. A useful application in the CAD of footwear is demonstrated as a motivation for this work. A simple software program has been implemented to test the operator, and examples are provided to demonstrate its use.

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