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Rozprawy doktorskie na temat „Hilbert space operators”

Autor: Grafiati

Data publikacji: 6 września 2023

Data aktualizacji: 31 lipca 2025

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1

邱彩娜 and Choi-nai Charlies Tu. "Generalized spectral norms of Hilbert space operators." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31220010.

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2

Tu, Choi-nai Charlies. "Generalized spectral norms of Hilbert space operators /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19737452.

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3

Tian, Feng. "On commutativity of unbounded operators in Hilbert space." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1095.

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We study several unbounded operators with view to extending von Neumann's theory of deficiency indices for single Hermitian operators with dense domain in Hilbert space. If the operators are non-commuting, the problems are difficult, but special cases may be understood with the use representation theory. We will further study the partial derivative operators in the coordinate directions on the L2 space on various covering surfaces of the punctured plane. The operators are defined on the common dense domain of C∞ functions with compact support, and they separately are essentially selfadjoint, b

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4

Kiteu, Marco M. "Orbits of operators on Hilbert space and some classes of Banach spaces." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1341850621.

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5

Hansen, A. C. "On the approximation of spectra of linear Hilbert space operators." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603665.

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The main topic of this thesis is how to approximate and compute spectra of linear operators on separable Hilbert spaces. We consider several approaches including the finite section method, an infinite-dimensional version of the QR algorithm, as well as pseudospectral techniques. Several new theorems about convergence of the finite section method (and variants of it) for self-adjoint problems are obtained together with a rigorous analysis of the infinite-dimensional QR algorithm for normal operators. To attack the general spectral problem we look to the pseudospectral theory and introduce the c

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6

Guven, Ayse. "Quantitative perturbation theory for compact operators on a Hilbert space." Thesis, Queen Mary, University of London, 2016. http://qmro.qmul.ac.uk/xmlui/handle/123456789/23197.

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This thesis makes novel contributions to a problem of practical and theoretical importance, namely how to determine explicitly computable upper bounds for the Hausdorff distance of the spectra of two compact operators on a Hilbert space in terms of the distance of the two operators in operator norm. It turns out that the answer depends crucially on the speed of decay of the sequence of singular values of the two operators. To this end, 'compactness classes', that is, collections of operators the singular values of which decay at a certain speed, are introduced and their functional analytic pro

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7

Alcántara, Bode Julio. "A criteria of completeness for compact operators in Hilbert space." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97122.

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A necessary and sufficient condition is given for completeness of the set of eigenfunctions and generalized eigenfunctions associated to the non zero eigenvalues of a compact operator on a Hilbert Space.

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8

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

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9

Raney, Michael W. "Abstract backward shifts of finite multiplicity /." view abstract or download file of text, 2002. http://wwwlib.umi.com/cr/uoregon/fullcit?p3061962.

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Thesis (Ph. D.)--University of Oregon, 2002.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaf 55). Also available for download via the World Wide Web; free to University of Oregon users.

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10

Kazemi, Parimah. "Compact Operators and the Schrödinger Equation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5453/.

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In this thesis I look at the theory of compact operators in a general Hilbert space, as well as the inverse of the Hamiltonian operator in the specific case of L2[a,b]. I show that this inverse is a compact, positive, and bounded linear operator. Also the eigenfunctions of this operator form a basis for the space of continuous functions as a subspace of L2[a,b]. A numerical method is proposed to solve for these eigenfunctions when the Hamiltonian is considered as an operator on Rn. The paper finishes with a discussion of examples of Schrödinger equations and the solutions.

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11

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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12

Atim, Alexandru Gabriel Kallman Robert R. "Uniqueness results for the infinite unitary, orthogonal and associated groups." [Denton, Tex.] : University of North Texas, 2008. http://digital.library.unt.edu/permalink/meta-dc-6136.

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13

Höber, Marc [Verfasser]. "Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes / Marc Höber." Mainz : Universitätsbibliothek der Johannes Gutenberg-Universität Mainz, 2007. http://d-nb.info/1225402042/34.

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14

Atim, Alexandru Gabriel. "Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups." Thesis, University of North Texas, 2008. https://digital.library.unt.edu/ark:/67531/metadc6136/.

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Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the projective orthogonal group and for the real isometry group. The theorem fails for U(H) if H is finite

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15

Chakmak, Ryan. "Eigenvalues and Approximation Numbers." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2167.

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While the spectral theory of compact operators is known to many, knowledge regarding the relationship between eigenvalues and approximation numbers might be less known. By examining these numbers in tandem, one may develop a link between eigenvalues and l^p spaces. In this paper, we develop the background of this connection with in-depth examples.

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16

Merghni, Lobna. "Propriétés spectrales des opérateurs de composition et opérateurs de Hankel." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0029.

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Dans cette thèse nous nous intéressons aux opérateurs de composition sur les espaces de Hardy et Dirichlet et aux opérateurs de Hankel sur les espaces des fonction polyanalytiques. On s’'intéresse à l’'opérateur de composition sur les espaces de Dirichlet : $mathcal{D}_alpha=\left{f \in Hol(D): |f|_alpha^{2}=| f(0)| ^{2}+int_{D}| f'(z)| ^{2}dA_alpha(z)<br>In this thesis we focus on the composition operators on Hardy and Dirichlet spaces and Hankel operators on spaces of polyanalytiques functions. We are interested in the composition operator on the Dirichlet spaces: $$ mathcal{D}_alpha=left{ f

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17

Khalil, Asma Mohammed. "Structure of scalar-type operators on Lp spaces and well-bounded operators on Hilbert spaces." Thesis, University of Edinburgh, 2002. http://hdl.handle.net/1842/10983.

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It is known that every scalar-type spectral operator on a Hilbert space <i>H</i> is similar to a multiplication operator on some <i>L</i><sup>2</sup><i> </i>space. The purpose of the main theorem in Chapter 2 of this thesis is to show that every scalar-type spectral operator on an <i>L</i><sup>1</sup> space whose spectral measure has finite multiplicity is similar to a multiplication operator on the same <i>L</i><sup>1</sup> space. Then we prove a similar result for scalar-type spectral operators on <i>L<sup>p</sup> </i>(Ω, S<sub>Ω</sub>, <i>m</i>), <i>p </i>≠<i> </i> 2, 1 < <i>p</i> < ∞, with

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18

Boulton, Lyonell. "Topics in the spectral theory of non adjoint operators." Thesis, King's College London (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272412.

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19

Hansmann, Marcel. "On the discrete spectrum of linear operators in Hilbert spaces." Clausthal-Zellerfeld Universitätsbibliothek Clausthal, 2010. http://d-nb.info/1001898664/34.

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20

Zandler, Andersson Nils. "Boundedness of a Class of Hilbert Operators on Modulation Spaces." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-84932.

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In this work we take interest in frames and modulation spaces. On the basis of their properties, we show how frame expansions can be used to prove the boundedness of a particular class of Hilbert operators on modulation spaces taking advantage of the special category of piece-wise polynomial functions known as B-splines.

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21

Khadivi, Mohammad Reza. "Operator theory and infinite networks." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/30019.

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22

Hansmann, Marcel [Verfasser]. "On the discrete spectrum of linear operators in Hilbert spaces / Marcel Hansmann." Clausthal-Zellerfeld : Universitätsbibliothek Clausthal, 2010. http://d-nb.info/1001898664/34.

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23

Srithharan, T. "Theory and applications of Hilbert's and Thompson's metrics to positive operators in ordered spaces." Thesis, University of Sussex, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262302.

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24

Hofmann, B., and O. Scherzer. "Local Ill-Posedness and Source Conditions of Operator Equations in Hilbert Spaces." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800957.

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The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods fo

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25

Formisano, Teresa. "Minimax in the theory of operators on Hilbert spaces and Clarkson-McCarthy estimates for lq (Sp) spaces of operators in the Schatten ideals." Thesis, London Metropolitan University, 2014. http://repository.londonmet.ac.uk/1099/.

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The main results in this thesis are the minimax theorems for operators in Schatten ideals of compact operators acting on separable Hilbert spaces, generalized Clarkson-McCarthy inequalities for vector lq-spaces lq (Sp) of operators from Schatten ideals Sp, inequalities for partitioned operators and for Cartesian decomposition of operators. All Clarkson-McCarthy type inequalities are in fact some estimates on the norms of operators acting on the spaces lq (Sp) or from one such space into another.

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26

Cassier, Gilles. "Algebres duales d'operateurs sur l'espace de hilbert." Paris 6, 1988. http://www.theses.fr/1988PA066122.

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Etude des algebres duales d'operateurs sur l'espace de hilbert subdivisee en quatre parties. La 1ere traite des questions relatives aux topologies definies sur l'algebre duale engendree par un operateur et a la classification proposee par h. Bercovici, c. Foias et c. Pearcy de ces algebres. On montre au cours de la 2eme partie des proprietes de convexite de l'image numerique simultanee lorsque les operateurs se trouvent dans une algebre duale uniforme. Elles sont en defaut si l'algere duale n'est pas unifrome. La 3eme contient quelques remarques sur les algebres duales engendrees par un seul o

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27

Hofmann, B. "On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801185.

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In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed.

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28

Abdillah, Said Amana. "Extensions au cadre Banachique de la notion d'opérateur de Hilbert-Schmidt." Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR14622/document.

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Cette thèse est consacrée à l’extension au cadre Banachique de la notion d’opérateur de Hilbert-Schmidt. Dans un premier temps, on étudie d’une part les opérateurs p-sommants dans un espace de Banach X vers un autre espace de Banach Y et d’autre part, les opérateurs gamma-radonifiants dans un espace de Hilbert vers un autre espace de Banach.Dans un second temps, on s'intéresse aux opérateurs gamma-sommants dans des espaces de Banach, qui coïncident avec les opérateurs de Rademacher-bornés, ce qui nous amène aux opérateurs presque sommants. Enfin, on en déduit plusieurs généralisations naturell

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29

Giulini, Ilaria. "Generalization bounds for random samples in Hilbert spaces." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0026/document.

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Ce travail de thèse porte sur l'obtention de bornes de généralisation pour des échantillons statistiques à valeur dans des espaces de Hilbert définis par des noyaux reproduisants. L'approche consiste à obtenir des bornes non asymptotiques indépendantes de la dimension dans des espaces de dimension finie, en utilisant des inégalités PAC-Bayesiennes liées à une perturbation Gaussienne du paramètre et à les étendre ensuite aux espaces de Hilbert séparables. On se pose dans un premier temps la question de l'estimation de l'opérateur de Gram à partir d'un échantillon i. i. d. par un estimateur robu

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30

Agora, Elona. "Boundedness of the Hilbert Transform on Weighted Lorentz Spaces." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/108930.

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The main goal of this thesis is to characterize the weak-type (resp. strong-type) boundedness of the Hilbert transform H on weighted Lorentz spaces Λpu(w). The characterization is given in terms of some geometric conditions on the weights u and w and the weak-type (resp. strong-type) boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results extend and unify simultaneously the theory of the boundedness of H on weighted Lebesgue spaces Lp(u) and Muckenhoupt weights Ap, and the theory on classical Lorentz spaces Λp(w) and Ariño-Muckenhoupt weights Bp.<br>Títol:

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31

Seddik, Ameur. "Intersection de l'adhérence de l'image d'une dérivation "delta"A avec le commutant de A* dans des cas particuliers." Montpellier 2, 1988. http://www.theses.fr/1988MON20107.

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A un element a de l(h) algebre des operateurs lineaires bornes definis sur l'espace de hilbert complexe h, on associe l'operateur de derivation delta ::(a) defini sur l(h) par: delta ::(a)(x)=ax-xa, x appartient a l(h). L'objet de cette etude est de trouver des operateurs de l(h) appartenant a la classe m=(a appartient a l(h):r(delta ::(a)) inter (a*)'=(o)). On a montre que cette classe contient les operateurs de la forme a cercle+b, ou p(a)=o pour un certain polynome p du second degre et b appartient a m, les operateurs de jordan d'ordre quelconque, et on donne quelques exemples d'operateurs

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32

Niedzialomski, Robert. "Extension of positive definite functions." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/2595.

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Let $\Omega\subset\mathbb{R}^n$ be an open and connected subset of $\mathbb{R}^n$. We say that a function $F\colon \Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, is positive definite if for any $x_1,\ldots,x_m\in\Omega$ and any $c_1,\ldots,c_m\in \mathbb{C}$ we have that $\sum_{j,k=1}^m F(x_j-x_k)c_j\overline{c_k}\geq 0$. Let $F\colon\Omega-\Omega\to\mathbb{C}$ be a continuous positive definite function. We give necessary and sufficient conditions for $F$ to have an extension to a continuous

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33

Acevedo, Jeovanny de Jesus Muentes. "O fluxo espectral de caminhos de operadores de Fredholm auto-adjuntos em espaços de Hilbert." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-01122017-214259/.

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O objetivo principal desta dissertação é apresentar o fluxo espectral de um caminho de operadores de Fredholm auto-adjuntos em um espaço de Hilbert e suas propriedades. Pelos resultados clássicos de teoria espectral, sabemos que se H é um espaço de Hilbert e L : H &#8594 H é um operador linear, limitado e auto-adjunto, H pode ser escrito como soma direta ortogonal H+(L)&#8853 H-(L)&#8853 Ker L, onde H+(L) e H-(L) são os subespaços espectrais positivo e negativo de L, respectivamente. No trabalho damos uma definição de fluxo espectral baseada na decomposição acima, aprofundando as conexões des

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34

Lambert, Alex. "Learning function-valued functions in reproducible kernel Hilbert spaces with integral losses : Application to infinite task learning." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAT016.

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Les méthodes à noyaux sont au coeur de l'apprentissage statistique. Elles permettent de modéliser des fonctions à valeurs réelles dans des espaces de fonctions à fort potentiel représentatif, sur lesquels la minimisation de risques empiriques régularisés est possible et produit des estimateurs dont le comportement statistique est largement étudié. Lorsque les sorties ne sont plus réelles mais de plus grande dimension, les Espaces de Hilbert à Noyaux Reproduisants à valeurs vectorielles (vv-RKHSs) basés sur des Noyaux à Valeurs Opérateurs (OVKs) fournissent des espaces de fonctions similaires e

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35

Hofmann, B., and G. Fleischer. "Stability Rates for Linear Ill-Posed Problems with Convolution and Multiplication Operators." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800987.

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In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete leas

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36

Amaya, Austin J. "Beurling-Lax Representations of Shift-Invariant Spaces, Zero-Pole Data Interpolation, and Dichotomous Transfer Function Realizations: Half-Plane/Continuous-Time Versions." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27636.

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Given a full-range simply-invariant shift-invariant subspace <i>M</i> of the vector-valued <i>L<sup>2</sup></i> space on the unit circle, the classical Beurling-Lax-Halmos (BLH) theorem obtains a unitary operator-valued function <i>W</i> so that <i>M</i> may be represented as the image of of the Hardy space <i>H<sup>2</sup></i> on the disc under multiplication by <i>W</i>. The work of Ball-Helton later extended this result to find a single function representing a so-called dual shift-invariant pair of subspaces <i>(M,M<sup>Ã </sup>)</i> which together form a direct-sum decomposition of <i>L<su

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37

Dora, Seleši. "Uopšteni stohastički procesi u beskonačno-dimenzionalnim prostorima sa primenama na singularne stohastičke parcijalne diferencijalne jednačine." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2007. https://www.cris.uns.ac.rs/record.jsf?recordId=6018&source=NDLTD&language=en.

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Doktorska disertacija je posvećena raznim klasama uop&scaron;tenih stohastičkih procesa i njihovim primenama na re&scaron;avanje singularnih stohastičkih parcijalnih diferencijalnih jednačina. U osnovi, disertacija se može podeliti na dva dela. Prvi deo disertacije (Glava 2) je posvećen strukturnoj karakterizaciji uop&scaron;tenih stohastičkih procesa u vidu haos ekspanzije i integralne reprezentacije. Drugi deo disertacije (Glava 3) čini primena dobijenih rezultata na re·savanje stohastičkog Dirihleovog problema u kojem se množenje modelira Vikovim proizvodom, a koefcijenti eliptičnog

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38

Smith, Lidia. "On Orbits of Operators on Hilbert Space." 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-08-842.

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In this dissertation we treat some problems about possible density of orbits for non-hypercyclic operators and we enlarge the class of known non-orbit-transitive operators. One of the questions related to hypercyclic operators that we answer is whether the density (in the set of positive real numbers) of the norms of the elements in the orbit for each nonzero vector in the Hilbert space is sufficient to imply that at least one vector has orbit dense in the Hilbert space. We show that the density of the norms is not a sufficient condition to imply hypercyclicity by constructing a weighted bilat

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39

Stephen, Matthew A. "Spectral Theory for Bounded Operators on Hilbert Space." 2013. http://hdl.handle.net/10222/35345.

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This thesis is an exposition of spectral theory for bounded operators on Hilbert space. Detailed proofs are given for the functional calculus, the multiplication operator, and the projection-valued measure versions of the spectral theorem for self-adjoint bounded operators. These theorems are then generalized to finite sequences of self-adjoint and commuting bounded operators. Finally, normal bounded operators are discussed, as a particular case of the generalization.

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40

Hung, Ching-Nam. "The numerical range and the core of Hilbert-space operators." 2004. http://link.library.utoronto.ca/eir/EIRdetail.cfm?Resources__ID=94714&T=F.

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41

Singh, Pravin. "Polynomial approximations to functions of operators." Thesis, 1994. http://hdl.handle.net/10413/5140.

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To solve the linear equation Ax = f, where f is an element of Hilbert space H and A is a positive definite operator such that the spectrum (T (A) ( [m,M] , we approximate -1 the inverse operator A by an operator V which is a polynomial in A. Using the spectral theory of bounded normal operators the problem is reduced to that of approximating a function of the real variable by polynomials of best uniform approximation. We apply two different techniques of evaluating A-1 so that the operator V is chosen either as a polynomial P (A) when P (A) approximates the n n function 1/A on the interval [m,

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42

Carter, James Michael. "Commutants of composition operators on the Hardy space of the disk." 2013. http://hdl.handle.net/1805/3659.

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Indiana University-Purdue University Indianapolis (IUPUI)<br>The main part of this thesis, Chapter 4, contains results on the commutant of a semigroup of operators defined on the Hardy Space of the disk where the operators have hyperbolic non-automorphic symbols. In particular, we show in Chapter 5 that the commutant of the semigroup of operators is in one-to-one correspondence with a Banach algebra of bounded analytic functions on an open half-plane. This algebra of functions is a subalgebra of the standard Newton space. Chapter 4 extends previous work done on maps with interior fixed point t

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43

Ghara, Soumitra. "Decomposition of the tensor product of Hilbert modules via the jet construction and weakly homogeneous operators." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4909.

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Let ½ Cm be a bounded domain and K :£!C be a sesqui-analytic function. We show that if ®,¯ È 0 be such that the functions K® and K¯, defined on £, are non-negative definite kernels, then theMm(C) valued function K(®,¯)(z,w) :Æ K®Å¯(z,w) ³ ¡ @i¯@ j logK ¢ (z,w) ´m i , jÆ1 , z,w 2, is also a non-negative definite kernel on £. Then a realization of the Hilbert space (H,K(®,¯)) determined by the kernel K(®,¯) in terms of the tensor product (H,K®)(H,K¯) is obtained. For two reproducing kernel Hilbert modules (H,K1) and (H,K2), let An, n ¸ 0, be the submodule of the Hilbert mo

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44

Bhattacharjee, Monojit. "Analytic Models, Dilations, Wandering Subspaces and Inner Functions." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4241.

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This thesis concerns dilation theory, analytic models, joint invariant subspaces, reproducing kernelHilbert spaces and multipliers associated to commuting tuples of bounded linear operators on Hilbert spaces. The main contribution of this thesis is twofold: dilation and analytic model theory for n-tuples of (1) commuting contractions (in the setting of the unit polydisc), and (2) commuting row contractions (in the setting of the unit ball). On n-tuples of commuting contractions: We study analytic models of operators with some positivity assumptions and quotient modules of function Hilbert spac

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Martin, Robert. "Bandlimited functions, curved manifolds, and self-adjoint extensions of symmetric operators." Thesis, 2008. http://hdl.handle.net/10012/3698.

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Sampling theory is an active field of research that spans a variety of disciplines from communication engineering to pure mathematics. Sampling theory provides the crucial connection between continuous and discrete representations of information that enables one store continuous signals as discrete, digital data with minimal error. It is this connection that allows communication engineers to realize many of our modern digital technologies including cell phones and compact disc players. This thesis focuses on certain non-Fourier generalizations of sampling theory and their applications. In

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46

Thompson, Derek Allen. "Restrictions to Invariant Subspaces of Composition Operators on the Hardy Space of the Disk." 2014. http://hdl.handle.net/1805/3881.

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Indiana University-Purdue University Indianapolis (IUPUI)<br>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 se

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47

Pal, Sourav. "Dilations, Functoinal Model And A Complete Unitary Invariant Of A r-contraction." Thesis, 2011. https://etd.iisc.ac.in/handle/2005/2182.

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A pair of commuting bounded operators (S, P) for which the set r = {(z 1 +z 2,z 1z 2) : |z 1| ≤1, |z 2| ≤1} C2 is a spectral set, is called a r-contraction in the literature. For a contraction P and a bounded commutant S of P, we seek a solution of the operator equation S –S*P = (I –P*P)½ X(I –P*P)½ where X is a bounded operator on Ran(I – P*P)½ with numerical radius of X being not greater than 1. We show the existence and uniqueness of solution to the operator equation above when (S,P) is a r-contraction. We call the unique solution, the fundamental operator of the r-contraction (S,P).

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Pal, Sourav. "Dilations, Functoinal Model And A Complete Unitary Invariant Of A r-contraction." Thesis, 2011. http://etd.iisc.ernet.in/handle/2005/2182.

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A pair of commuting bounded operators (S, P) for which the set r = {(z 1 +z 2,z 1z 2) : |z 1| ≤1, |z 2| ≤1} C2 is a spectral set, is called a r-contraction in the literature. For a contraction P and a bounded commutant S of P, we seek a solution of the operator equation S –S*P = (I –P*P)½ X(I –P*P)½ where X is a bounded operator on Ran(I – P*P)½ with numerical radius of X being not greater than 1. We show the existence and uniqueness of solution to the operator equation above when (S,P) is a r-contraction. We call the unique solution, the fundamental operator of the r-contraction (S,P). As

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Hota, Tapan Kumar. "Subnormality and Moment Sequences." Thesis, 2012. http://etd.iisc.ac.in/handle/2005/3242.

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In this report we survey some recent developments of relationship between Hausdorﬀ moment sequences and subnormality of an unilateral weighted shift operator. Although discrete convolution of two Haudorﬀ moment sequences may not be a Hausdorﬀ moment sequence, but Hausdorﬀ convolution of two moment sequences is always a moment sequence. Observing from the Berg and Dur´an result that the multiplication operator on Is subnormal, we discuss further work on the subnormality of the multiplication operator on a reproducing kernel Hilbert space, whose kernel is a point-wise product of two diagonal po

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50

Hota, Tapan Kumar. "Subnormality and Moment Sequences." Thesis, 2012. http://hdl.handle.net/2005/3242.

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In this report we survey some recent developments of relationship between Hausdorﬀ moment sequences and subnormality of an unilateral weighted shift operator. Although discrete convolution of two Haudorﬀ moment sequences may not be a Hausdorﬀ moment sequence, but Hausdorﬀ convolution of two moment sequences is always a moment sequence. Observing from the Berg and Dur´an result that the multiplication operator on Is subnormal, we discuss further work on the subnormality of the multiplication operator on a reproducing kernel Hilbert space, whose kernel is a point-wise product of two diagonal po

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