Dissertations / Theses: 'Spectral theory (Mathematics)'

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Zinchenko, Maksym. "Topics in spectral and inverse spectral theory." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4460.

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Thesis (Ph.D.)--University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 2, 2007) Vita. Includes bibliographical references.

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Ghaemi, Mohammad B. "Spectral theory of linear operators." Thesis, Connect to e-thesis, 2000. http://theses.gla.ac.uk/998/.

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Thesis (Ph.D.) - University of Glasgow, 2000.
Ph.D. thesis submitted to the Department of Mathematics, University of Glasgow, 2000. Includes bibliographical references. Print version also available.

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Muzundu, Kelvin. "Spectral theory in commutatively ordered banach algebras." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71619.

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Nath, Jiban Kumar. "Spectral theory of non-selfadjoint operators." Thesis, King's College London (University of London), 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.271218.

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Slegers, Wouter. "Spectral Theory for Perron-Frobenius operators." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-396647.

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Strömberg, Roland. "Spectral Theory for Bounded Self-adjoint Operators." Thesis, Uppsala University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121364.

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Khan, Saadia. "Spectral theory and subordinacy of infinite matrices." Thesis, University of Hull, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314651.

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Tembo, Isaac Daniel. "Aspects of spectral theory for algebras of measurable operators." Doctoral thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/4934.

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Includes abstract.
Includes bibliographical references (p. 124-129).
The spectral theory for bounded normal operators on a Hilbert space and the various functional calculi for such operators is closely related to the representation theory of commutative C*- and von Neumann algebras as algebras of bounded continuous or measurable functions. For unbounded operators the corresponding theory leads to algebras of unbounded densely defined operators. The thesis looks at aspects of spectral theory in the non-commutative generalisations of these algebras. Given a von Neumann algebra M, there are various notions of measurability for operators affiliated with M, and the measurable operators of a particular kind form an involutive algebra under the strong sum and product. Algebras of this kind can usually be equipped with a topology modelled on the topology of convergence in measure under which they become topological algebras. The emphasis in this thesis is on a semifinite von Neumann algebra M equipped with a semi-finite faithful normal trace τ and the corresponding algebra M~ of τ-measurable operators.

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Linder, Kevin A. (Kevin Andrew). "Spectral multiplicity theory in nonseparable Hilbert spaces : a survey." Thesis, McGill University, 1991. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60478.

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Spectral multiplicity theory solves the problem of unitary equivalence of normal operate on a Hilbert space ${ cal H}$ by associating with each normal operator N a multiplicity function, such that two operators are unitarily equivalent if and only if their multiplicity functions are equal. This problem was first solved in the classical case in which ${ cal H}$ is separable by Hellinger in 1907, and in the general case in which ${ cal H}$ is nonseparable by Wecken in 1939. This thesis develops the later versions of multiplicity theory in the nonseparable case given by Halmos and Brown, and gives the simplification of Brown's version to the classical theory. Then the versions of Halmos and Brown are shown directly to be equivalent. Also, the multiplicity function of Brown is expressed in terms of the multiplicity function of Halmos.

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Markett, Simon A. "The Grayson spectral sequence for hermitian K-theory." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/74068/.

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Let R be a regular ring such that 2 is invertible. We construct a spectral sequence converging to the hermitian K-theory, alias the Grothendieck-Witt theory, of R. In particular, we construct a tower for the hermitian K-groups in even shifts, whose terms are given by the hermitian K-theory of automorphisms. The spectral sequence arises as the homotopy spectral sequence of this tower and is analogous to Grayson’s version of the motivic spectral sequence [Gra95]. Further, we construct similar towers for the hermitian K-theory in odd shifts if R is a field of characteristic different from 2. We show by a counter example that the arising spectral sequence does not behave as desired. We proceed by proposing an alternative version for the tower and verify its correctness in weight 1. Finally we give a geometric representation of the (hermitian) K-theory of automorphisms in terms of the general linear group, the orthogonal group, or in terms of e-symmetric matrices, respectively. The K-theory of automorphisms can be identified with motivic cohomology if R is local and of finite type over a field. Therefore the hermitian K-theory of automorphisms as presented in this thesis is a candidate for the analogue of motivic cohomology in the hermitian world.

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Vaillant, Boris. "Index- and spectral theory for manifolds with generalized fibred cusps." Bonn : Mathematisches Institut der Universität, 2001. http://catalog.hathitrust.org/api/volumes/oclc/51691852.html.

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Rittenhouse, Michelle L. "Properties and Recent Applications in Spectral Graph Theory." VCU Scholars Compass, 2008. http://scholarscompass.vcu.edu/etd/1126.

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There are numerous applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, the importance of eigenvalues in protein structures, and the aid that the spectra of a graph provides when coloring a graph are covered, as well as others.The key definitions and properties of graph theory are introduced. Important aspects of graphs, such as the walks and the adjacency matrix are explored. In addition, bipartite graphs are discussed along with properties that apply strictly to bipartite graphs. The main focus is on the characteristic polynomial and the eigenvalues that it produces, because most of the applications involve specific eigenvalues. For example, if isomers are organized according to their eigenvalues, a pattern comes to light. There is a parallel between the size of the eigenvalue (in comparison to the other eigenvalues) and the maximum degree of the graph. The maximum degree of the graph tells us the most carbon atoms attached to any given carbon atom within the structure. The Laplacian matrix and many of its properties are discussed at length, including the classical Matrix Tree Theorem and Cayley's Tree Theorem. Also, an alternative approach to defining the Laplacian is explored and compared to the traditional Laplacian.

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Borovyk, Vita. "Box approximation and related techniques in spectral theory." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5566.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2008.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 2, 2009) Vita. Includes bibliographical references.

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Owen, Mark Philip. "Topics in the spectral theory of fourth order elliptic differential operators." Thesis, King's College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244119.

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Green, Edward L. "Spectral theory of laplace-beltrami operators with periodic metrics." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/29187.

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Christodoulides, Yiannis Takis. "Spectral theory of Herglotz functions and their compositions, and the Schrödinger equation." Thesis, University of Hull, 2001. http://hydra.hull.ac.uk/resources/hull:5406.

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In this thesis we generalize the theory of value distribution associated to a Herglotz function. Compositions of Herglotz functions are studied, and some results regarding the integral representation of a composed Herglotz function are obtained. Properties of spectral measures corresponding to Herglotz functions are derived, and an application to the Schrödinger equation is given.

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Arrieta, Jose M. "Spectral properties of schrodinger operators under perturbations of the domain." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/29459.

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Jonsson, Erik. "Numerical Range of Square Matrices : A Study in Spectral Theory." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-157661.

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In this thesis, we discuss important results for the numerical range of general square matrices. Especially, we examine analytically the numerical range of complex-valued $2 \times 2$ matrices. Also, we investigate and discuss the Gershgorin region of general square matrices. Lastly, we examine numerically the numerical range and Gershgorin regions for different types of square matrices, both contain the spectrum of the matrix, and compare these regions, using the calculation software Maple.

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Baker, Steven Jeffrey. "Spectral properties of displacement models." Birmingham, Ala. : University of Alabama at Birmingham, 2007. https://www.mhsl.uab.edu/dt/2007p/baker.pdf.

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Thesis (Ph. D.)--University of Alabama at Birmingham, 2007.
Additional advisors: Richard Brown, Ioulia Karpechina, Ryoichi Kawai, Boris Kunin. Description based on contents viewed Feb. 5, 2008; title from title screen. Includes bibliographical references (p. 73-75).

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Forbes, Keith. "Theory and efficient algorithms for image restoration and spectral estimation." Thesis, Queensland University of Technology, 1993. https://eprints.qut.edu.au/36704/1/36704_Digitised%20Thesis.pdf.

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Different approaches are used in tackling the two main areas of study outlined in this thesis report, image restoration and spectral estimation. They are, however, shown to be linked by the principle of Maximum Entropy (ME), the use of which is treated extensively for image restoration, especially in regard to the effect of noise on the solution. Direct image restoration is known to suffer severely from noise in the image due to the ill-condition of the restoring matrix. In the past however, while many ingenious techniques have been devised for overcoming this problem, the condition has not been adequately quantified. These techniques come under the area of smoothing algorithms and ME is one such method, albeit a fundamental one since ME is involved in image formation and is claimed to be the only consistent method. It is shown how to calculate several condition numbers of a restoring matrix and a condition number (Ks) which is particularly suitable for additive white noise ( of standard deviation σ ) in the image is introduced. The standard deviation of the error in any element of the predicted object vector is then Ks.σ. Direct restoration of 1-dimensional(lD) and 2-dimensional(2D) images is studied in order that the condition of the restoring matrix can be calculated. In the 2D case, the use of circulant matrices has produced powerful algorithms for finding eigenvalues and inverses. It is shown that some Point Spread Functions (PSFs) produce well-conditioned restoring matrices. Most PSFs, however, produce restoring matrices which can be singular or very ill-conditioned in some cases. Conditions for these occurrences have been developed. Surprisingly, the size of the image used can have a big effect on the condition. Smoothing algorithms have been looked at briefly with a view to studying the effect these algorithms have on the condition of the restoration. Maximum entropy methods of restoration have been shown to be very robust m the presence of noise in the image, but again this has not been quantified except in special cases. In this thesis report, several ME algorithms are implemented and new algorithms are devised for calculating the condition numbers. Differing from direct restoration, the condition is not independent of the object or certain parameters used in the ME method, but the results show that this dependence is not great and the method is robust over a wide range. New techniques, based on the theory of Pick Functions, have been developed for estimating the frequencies, amplitudes, and phases of harmonics present in a lD signal. An expression for the entropy of a continuous-parameter stochastic process is obtained and a study made of the connection between the Pick function method and the spectral estimation based on maximising the entropy. An intermediate stage in the calculation of the harmonics is the use of the Taylor series coefficients of the covariance function and these are obtained from the signal by polynomial regression using orthogonal polynomials. The regression is carried out recursively. The effect additive white noise in the signal has on the predicted results is also studied. As for image restoration above, a matrix which premultiplies the noise vector to produce a vector giving the change in the solution has been obtained. The condition of this matrix is determined. As for the ME algorithms, the condition is not a single number but a vector K8 • This causes the standard deviation of the noise in the signal (σ) to be multiplied by different values depending on which parameter of the solution is being determined. Also, as in the ME case, the elements of ~ are not independent of the predicted solutions. In particular, close spectral peaks cause the multipliers of a to increase dramatically. The Burg method of spectral estimation of discrete-parameter lD signals is based on maximising the entropy subject to the covariance constraints. The resulting ME spectral density is that of an autoregressive (AR) process. The problem is therefore to estimate the coefficients of an AR model. An advantage of this ME approach is the availability of the Levinson recursion in estimating efficiently the AR coefficients. This thesis develops several new Levinson-type algorithms for spatial AR models. A quarter-plane (QP) ordering or a nonsymmetric half-plane (NSHP) ordering is assumed in defining a spatial AR process. The algorithms are recursive in both directions in the QP case and all three directions simultaneously in the NSHP case, and hence are computationallyefficient. The algorithms have been implemented (in the QP case) and used in estimating the spectral density of some simple spatial processes.

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Lan, Chao-ho. "Radiative combined-mode heat transfer in a multi-dimensional participating medium using spectral methods /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004312.

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Wells, Allan R. "Spectral analysis of multi-spindle machining heads /." Online version of thesis, 1994. http://hdl.handle.net/1850/12019.

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Belt, Dustin David. "Topics on the Spectral Theory of Automorphic Forms." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1423.pdf.

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David, Jean-Yves. "Modern spectral analysis techniques for blood flow velocity and spectral measurements with a 20 MHZ pulsed doppler ultrasound catheter." Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/17791.

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Watson, Cody Edward. "On the Spectra of Momentum Operators." Wright State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=wright1398851401.

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Kanaan, Mona N. "Cross-spectral analysis for spatial point-lattice processes." Thesis, [n.p.], 2000. http://dart.open.ac.uk/abstracts/page.php?thesisid=94.

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Heymann, Retha. "Fredholm theory in general Banach algebras." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4265.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: This thesis is a study of a generalisation, due to R. Harte (see [9]), of Fredholm theory in the context of bounded linear operators on Banach spaces to a theory in a Banach algebra setting. A bounded linear operator T on a Banach space X is Fredholm if it has closed range and the dimension of its kernel as well as the dimension of the quotient space X/T(X) are finite. The index of a Fredholm operator is the integer dim T−1(0)−dimX/T(X). Weyl operators are those Fredholm operators of which the index is zero. Browder operators are Fredholm operators with finite ascent and descent. Harte’s generalisation is motivated by Atkinson’s theorem, according to which a bounded linear operator on a Banach space is Fredholm if and only if its coset is invertible in the Banach algebra L(X) /K(X), where L(X) is the Banach algebra of bounded linear operators on X and K(X) the two-sided ideal of compact linear operators in L(X). By Harte’s definition, an element a of a Banach algebra A is Fredholm relative to a Banach algebra homomorphism T : A ! B if Ta is invertible in B. Furthermore, an element of the form a + b where a is invertible in A and b is in the kernel of T is called Weyl relative to T and if ab = ba as well, the element is called Browder. Harte consequently introduced spectra corresponding to the sets of Fredholm, Weyl and Browder elements, respectively. He obtained several interesting inclusion results of these sets and their spectra as well as some spectral mapping and inclusion results. We also convey a related result due to Harte which was obtained by using the exponential spectrum. We show what H. du T. Mouton and H. Raubenheimer found when they considered two homomorphisms. They also introduced Ruston and almost Ruston elements which led to an interesting result related to work by B. Aupetit. Finally, we introduce the notions of upper and lower semi-regularities – concepts due to V. M¨uller. M¨uller obtained spectral inclusion results for spectra corresponding to upper and lower semi-regularities. We could use them to recover certain spectral mapping and inclusion results obtained earlier in the thesis, and some could even be improved.
AFRIKAANSE OPSOMMING: Hierdie tesis is ‘n studie van ’n veralgemening deur R. Harte (sien [9]) van Fredholm-teorie in die konteks van begrensde lineˆere operatore op Banachruimtes tot ’n teorie in die konteks van Banach-algebras. ’n Begrensde lineˆere operator T op ’n Banach-ruimte X is Fredholm as sy waardeversameling geslote is en die dimensie van sy kern, sowel as di´e van die kwosi¨entruimte X/T(X), eindig is. Die indeks van ’n Fredholm-operator is die heelgetal dim T−1(0) − dimX/T(X). Weyl-operatore is daardie Fredholm-operatore waarvan die indeks gelyk is aan nul. Fredholm-operatore met eindige styging en daling word Browder-operatore genoem. Harte se veralgemening is gemotiveer deur Atkinson se stelling, waarvolgens ’n begrensde lineˆere operator op ’n Banach-ruimte Fredholm is as en slegs as sy neweklas inverteerbaar is in die Banach-algebra L(X) /K(X), waar L(X) die Banach-algebra van begrensde lineˆere operatore op X is en K(X) die twee-sydige ideaal van kompakte lineˆere operatore in L(X) is. Volgens Harte se definisie is ’n element a van ’n Banach-algebra A Fredholm relatief tot ’n Banach-algebrahomomorfisme T : A ! B as Ta inverteerbaar is in B. Verder word ’n Weyl-element relatief tot ’n Banach-algebrahomomorfisme T : A ! B gedefinieer as ’n element met die vorm a + b, waar a inverteerbaar in A is en b in die kern van T is. As ab = ba met a en b soos in die definisie van ’n Weyl-element, dan word die element Browder relatief tot T genoem. Harte het vervolgens spektra gedefinieer in ooreenstemming met die versamelings van Fredholm-, Weylen Browder-elemente, onderskeidelik. Hy het heelparty interessante resultate met betrekking tot insluitings van die verskillende versamelings en hulle spektra verkry, asook ’n paar spektrale-afbeeldingsresultate en spektraleinsluitingsresultate. Ons dra ook ’n verwante resultaat te danke aan Harte oor, wat verkry is deur van die eksponensi¨ele-spektrum gebruik te maak. Ons wys wat H. du T. Mouton en H. Raubenheimer verkry het deur twee homomorfismes gelyktydig te beskou. Hulle het ook Ruston- en byna Rustonelemente gedefinieer, wat tot ’n interessante resultaat, verwant aan werk van B. Aupetit, gelei het. Ten slotte stel ons nog twee begrippe bekend, naamlik ’n onder-semi-regulariteit en ’n bo-semi-regulariteit – konsepte te danke aan V. M¨uller. M¨uller het spektrale-insluitingsresultate verkry vir spektra wat ooreenstem met bo- en onder-semi-regulariteite. Ons kon dit gebruik om sekere spektrale-afbeeldingsresultate en spektrale-insluitingsresultate wat vroe¨er in hierdie tesis verkry is, te herwin, en sommige kon selfs verbeter word.

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Goertzen, Corissa Marie. "Operations on Infinite x Infinite Matrices and Their Use in Dynamics and Spectral Theory." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4849.

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By first looking at the orthonormal basis: Γ = {∑i 4 ibi ∈{0, 1}, finite sums} and the related orthonormal basis 5Γ = {5∑i 4i bi : bi ∈ {0, 1}, finite sums} we find several interesting relationships with the unitary matrix Uα,β arising from the operator U: Γ → 5Γ. Further, we investigate the relationships between U and the operators So : Γ → 4Γ defined by Soe4γ where eγ = e2ΠiΓ and S1: Γ → 4Γ+1 defined by S1eγ = e4γ+1. Most intriguing, we found that when taking powers of the aforementioned Uα,β matrix that although there are infinitely many 1's occurring in the entries of Uα,β only one such 1 occurs in the subsequent higher powers Ukα,β. This means that there are infinitely many γ ∈ Γ ∩ 5Γ, but only one such γ in the intersection Γ and 5kΓ, for k ≥ 2.

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Baker, Charles Edmond. "On the Determination of Spectral Properties of Certain Families of Operators." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1449153836.

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Pieper, Hannah E. "Comparing Two Thickened Cycles: A Generalization of Spectral Inequalities." Oberlin College Honors Theses / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528367417905844.

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Sundaramoorthy, Gopalakrishnan. "Improved techniques for bispectral reconstruction of signals /." Online version of print, 1990. http://hdl.handle.net/1850/11456.

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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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Koucherik, Elena. "Transference and Szego's theorem for measure preserving transformations." Diss., Columbia, Mo. : University of Missouri-Columbia, 2007. http://hdl.handle.net/10355/6018.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2007.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on March 11, 2008) Includes bibliographical references.

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Gaby, James Eliot. "Artificial intelligence applied to spectrum estimation." Thesis, Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/15715.

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Kwag, Jae-Hwan. "A comparative study of LP methods in MR spectral analysis /." free to MU campus, to others for purchase, 1999. http://wwwlib.umi.com/cr/mo/fullcit?p9962536.

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Tian, WeiDong 1965. "The spectral theory of ordinary derivations of K[X,Y] and weaker forms of the Jacobian conjucture /." Thesis, McGill University, 1999. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=36064.

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Let K be a field of characteristic zero, K[ x, y] be the polynomial ring in two variables. Let Delta f denote the K-derivation of K[ x, y] given by Deltaf(g) = J(f, g) = fxg y -- fygx, the Jacobian determinant of f, g with respect to the coordinate system x, y. The derivation Deltaf is a differential operator on K[x, y]. The main objective of this thesis is to develop the spectral theory of the differential operator Deltaf. More precisely, we not only determine the eigenvalues but also the structure of the eigenfunctions of Deltaf. In developing this spectral theory, we prove two weaker forms of the Jacobian Conjecture and establish some relations between the Jacobian Conjecture and our spectral theory.

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McGhie, Devin Burnell. "Some Spectral Properties of a Quantum Field Theoretic Hamiltonian." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/6586.

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We derive the ground-state eigenvalues and eigenvectors for a simplified version of the 1-D QED single electron-photon model that Glasgow et al recently developed [2]. This model still allows for meaningful interaction between electrons and photons while keeping only the minimum needed to do so. We investigate the interesting spectral properties of this model. We determine that the eigenvectors are orthogonal as one would expect and normalize them.

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Hollander, Michael Israel. "Linear numeration systems, finite beta expansions, and discrete spectrum of substitution dynamical systems /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/5747.

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Masum, Mohammad. "Vertex Weighted Spectral Clustering." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3266.

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Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to zero compared to the largest Fiedler coefficient of the graph. We propose a vertex-weighted spectral clustering algorithm which incorporates a vector of weights for each vertex of a given graph to form a vertex-weighted graph. The proposed algorithm predicts association of equidistant or nearly equidistant data points from both clusters while the unweighted clustering does not provide association. Finally, we implemented both the unweighted and the vertex-weighted spectral clustering algorithms on several data sets to show that the proposed algorithm works in general.

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Falkowski, Bogdan Jaroslaw. "Spectral Methods for Boolean and Multiple-Valued Input Logic Functions." PDXScholar, 1991. https://pdxscholar.library.pdx.edu/open_access_etds/1152.

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Spectral techniques in digital logic design have been known for more than thirty years. They have been used for Boolean function classification, disjoint decomposition, parallel and serial linear decomposition, spectral translation synthesis (extraction of linear pre- and post-filters), multiplexer synthesis, prime implicant extraction by spectral summation, threshold logic synthesis, estimation of logic complexity, testing, and state assignment. This dissertation resolves many important issues concerning the efficient application of spectral methods used in the computer-aided design of digital circuits. The main obstacles in these applications were, up to now, memory requirements for computer systems and lack of the possibility of calculating spectra directly from Boolean equations. By using the algorithms presented here these obstacles have been overcome. Moreover, the methods presented in this dissertation can be regarded as representatives of a whole family of methods and the approach presented can be easily adapted to other orthogonal transforms used in digital logic design. Algorithms are shown for Adding, Arithmetic, and Reed-Muller transforms. However, the main focus of this dissertation is on the efficient computer calculation of Rademacher-Walsh spectra of Boolean functions, since this particular ordering of Walsh transforms is most frequently used in digital logic design. A theory has been developed to calculate the Rademacher-Walsh transform from a cube array specification of incompletely specified Boolean functions. The importance of representing Boolean functions as arrays of disjoint ON- and DC- cubes has been pointed out, and an efficient new algorithm to generate disjoint cubes from non-disjoint ones has been designed. The transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. By such an approach each spectral coefficient can be calculated separately or all the coefficients can be calculated in parallel. These advantages are absent in the existing methods. The possibility of calculating only some coefficients is very important since there are many spectral methods in digital logic design for which the values of only a few selected coefficients are needed. Most of the current methods used in the spectral domain deal only with completely specified Boolean functions. On the other hand, all of the algorithms introduced here are valid, not only for completely specified Boolean functions, but for functions with don't cares. Don't care minterms are simply represented in the form of disjoint cubes. The links between spectral and classical methods used for designing digital circuits are described. The real meaning of spectral coefficients from Walsh and other orthogonal spectra in classical logic terms is shown. The relations presented here can be used for the calculation of different transforms. The methods are based on direct manipulations on Karnaugh maps. The conversion start with Karnaugh maps and generate the spectral coefficients. The spectral representation of multiple-valued input binary functions is proposed here for the first time. Such a representation is composed of a vector of Walsh transforms each vector is defined for one pair of the input variables of the function. The new representation has the advantage of being real-valued, thus having an easy interpretation. Since two types of codings of values of binary functions are used, two different spectra are introduced. The meaning of each spectral coefficient in classical logic terms is discussed. The mathematical relationships between the number of true, false, and don't care minterms and spectral coefficients are stated. These relationships can be used to calculate the spectral coefficients directly from the graphical representations of binary functions. Similarly to the spectral methods in classical logic design, the new spectral representation of binary functions can find applications in many problems of analysis, synthesis, and testing of circuits described by such functions. A new algorithm is shown that converts the disjoint cube representation of Boolean functions into fixed-polarity Generalized Reed-Muller Expansions (GRME). Since the known fast algorithm that generates the GRME, based on the factorization of the Reed-Muller transform matrix, always starts from the truth table (minterms) of a Boolean function, then the described method has advantages due to a smaller required computer memory. Moreover, for Boolean functions, described by only a few disjoint cubes, the method is much more efficient than the fast algorithm. By investigating a family of elementary second order matrices, new transforms of real vectors are introduced. When used for Boolean function transformations, these transforms are one-to-one mappings in a binary or ternary vector space. The concept of different polarities of the Arithmetic and Adding transforms has been introduced. New operations on matrices: horizontal, vertical, and vertical-horizontal joints (concatenations) are introduced. All previously known transforms, and those introduced in this dissertation can be characterized by two features: "ordering" and "polarity". When a transform exists for all possible polarities then it is said to be "generalized". For all of the transforms discussed, procedures are given for generalizing and defining for different orderings. The meaning of each spectral coefficient for a given transform is also presented in terms of standard logic gates. There exist six commonly used orderings of Walsh transforms: Hadamard, Rademacher, Kaczmarz, Paley, Cal-Sal, and X. By investigating the ways in which these known orderings are generated the author noticed that the same operations can be used to create some new orderings. The generation of two new Walsh transforms in Gray code orderings, from the straight binary code is shown. A recursive algorithm for the Gray code ordered Walsh transform is based on the new operator introduced in this presentation under the name of the "bi-symmetrical pseudo Kronecker product". The recursive algorithm is the basis for the flow diagram of a constant geometry fast Walsh transform in Gray code ordering. The algorithm is fast (N 10g2N additions/subtractions), computer efficient, and is implemented

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41

Engdahl, Erik. "Computation of resonance energies and spectral densities in the complex energy plane : application of complex scaling techniques for atoms, molecules and surfaces /." Uppsala : Uppsala Universitet, 1988. http://bibpurl.oclc.org/web/32938.

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42

Yoo, Hyungsuk. "Quality of the Volterra transfer function estimation /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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43

Tidblom, Jesper. "Improved Lp Hardy Inequalities." Doctoral thesis, Stockholm University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-615.

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Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).

The aim of this article is to prove a Hardy-type inequality, concerning functions in W_0^{1,p}(D) for some domain D in R^n, involving the volume of D and the distance to the boundary of D. The inequality is a generalization of a previously proved inequality by M. and T. Hoffmann-Ostenhof and A. Laptev, which dealt with the special case p=2.

Paper 2 : A Hardy inequality in the Half-space.

Here we prove a Hardy-type inequality in the half-space which generalize an inequality originally proved by V. Maz'ya to the so-called L^p case. This inequality had previously been conjectured by the mentioned author. We will also improve the constant appearing in front of the reminder term in the original inequality (which is the first improved Hardy inequality appearing in the litterature).

Paper 3 : Hardy type inequalities for Many-Particle systems.

In this article we prove some results about the constants appearing in Hardy inequalities related to many particle systems. We show that the problem of estimating the best constants there is related to some interesting questions from Geometrical combinatorics. The asymptotical behaviour, when the number of particles approaches infinity, of a certain quantity directly related to this, is also investigated.

Paper 4 : Various results in the theory of Hardy inequalities and personal thoughts.

In this article we give some further results concerning improved Hardy inequalities in Half-spaces and other conic domains. Also, some examples of applications of improved Hardy inequalities in the theory of viscous incompressible flow will be given.

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Savinien, Jean P. X. "Cohomology and K-theory of aperiodic tilings." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24732.

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Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008.
Committee Chair: Prof. Jean Bellissard; Committee Member: Prof. Claude Schochet; Committee Member: Prof. Michael Loss; Committee Member: Prof. Stavros Garoufalidis; Committee Member: Prof. Thang Le.

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Schubert, Luke. "Spectral properties of the Laplacian on p-forms on the Heisenberg group /." Title page, contents and abstract only, 1997. http://web4.library.adelaide.edu.au/theses/09PH/09phs384.pdf.

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46

Stanislavova, Milena. "Spectral mapping theorems and invariant manifolds for infinite-dimensional Hamiltonian systems /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9988702.

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47

Giusti, Chad David 1978. "Plumbers' knots and unstable Vassiliev theory." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10869.

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viii, 57 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
We introduce a new finite-complexity knot theory, the theory of plumbers' knots, as a model for classical knot theory. The spaces of plumbers' curves admit a combinatorial cell structure, which we exploit to algorithmically solve the classification problem for plumbers' knots of a fixed complexity. We describe cellular subdivision maps on the spaces of plumbers' curves which consistently make the spaces of plumbers' knots and their discriminants into directed systems. In this context, we revisit the construction of the Vassiliev spectral sequence. We construct homotopical resolutions of the discriminants of the spaces of plumbers knots and describe how their cell structures lift to these resolutions. Next, we introduce an inverse system of unstable Vassiliev spectral sequences whose limit includes, on its E ∞ - page, the classical finite-type invariants. Finally, we extend the definition of the Vassiliev derivative to all singularity types of plumbers' curves and use it to construct canonical chain representatives of the resolution of the Alexander dual for any invariant of plumbers' knots.
Committee in charge: Dev Sinha, Chairperson, Mathematics; Hal Sadofsky, Member, Mathematics; Arkady Berenstein, Member, Mathematics; Daniel Dugger, Member, Mathematics; Andrzej Proskurowski, Outside Member, Computer & Information Science

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Kronholm, William C. "The RO(G)-graded Serre spectral sequence /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2008. http://hdl.handle.net/1794/8284.

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Thesis (Ph. D.)--University of Oregon, 2008.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 71-72). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

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Savala, Paul. "Computing spectral data for Maass cusp forms using resonance." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/3182.

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The primary arithmetic information attached to a Maass cusp form is its Laplace eigenvalue. However, in the case of cuspidal Maass forms, the range that these eigenvalues can take is not well-understood. In particular it is unknown if, given a real number r, one can prove that there exists a primitive Maass cusp form with Laplace eigenvalue 1/4 + r2. Conversely, given the Fourier coeﬃcients of a primitive Maass cusp form f on Γ0(D), it is not clear whether or not one can determine its Laplace eigenvalue. In this paper we show that given only a ﬁnite number of Fourier coeﬃcients one can ﬁrst determine the level D, and then compute the Laplace eigenvalue to arbitrarily high precision. The key to our results will be understanding the resonance and rapid decay properties of Maass cusp forms. Let f be a primitive Maass cusp form with Fourier coeﬃcients λf (n). The resonance sum for f is given by SX(f;α;β) = Εn≥1λf(n)‑Φ(n/X) e(αnβ) where φ ∈ Cc∞((1, 2)) is a Schwartz function and α ∈ R and β, X > 0 are real numbers. Sums of this form have been studied for many diﬀerent classes of functions f, including holomorphic modular forms for SL(2, Z), and Maass cusp forms for SL(n,Z). In this paper we take f to be a primitive Maass cusp form for a congruence subgroup Γ0(D) ⊂ SL(2, Z). Thus our result extends the family of automorphic forms for which their resonance properties are understood. Similar analysis and algorithms can be easily implemented for holomorphic cusp forms for Γ0(D). Our techniques include Voronoi summation, weighted exponential sums, and asymptotics expansions of Bessel functions. We then use these estimates in a new application of resonance sums. In particular we show that given only limited information about a Maass cusp form f (in particular a ﬁnite list of high Fourier coeﬃcients), one can determine its level and estimate its spectral parameter, and thus its Laplace eigenvalue. This is done using a large parallel computing cluster running MATLAB and Mathematica

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Witt, Walter G. "Quantifying the Structure of Misfolded Proteins Using Graph Theory." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3244.

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The structure of a protein molecule is highly correlated to its function. Some diseases such as cystic fibrosis are the result of a change in the structure of a protein so that this change interferes or inhibits its function. Often these changes in structure are caused by a misfolding of the protein molecule. To assist computational biologists, there is a database of proteins together with their misfolded versions, called decoys, that can be used to test the accuracy of protein structure prediction algorithms. In our work we use a nested graph model to quantify a selected set of proteins that have two single misfold decoys. The graph theoretic model used is a three tiered nested graph. Measures based on the vertex weights are calculated and we compare the quantification of the proteins with their decoys. Our method is able to separate the misfolded proteins from the correctly folded proteins.

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Dissertations / Theses on the topic 'Spectral theory (Mathematics)'

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