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Rozprawy doktorskie na temat „Hilbert spaces”

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Data publikacji: 4 czerwca 2021
Data aktualizacji: 25 lipca 2025

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1

Wigestrand, Jan. "Inequalities in Hilbert Spaces." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9673.

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<p>The main result in this thesis is a new generalization of Selberg's inequality in Hilbert spaces with a proof. In Chapter 1 we define Hilbert spaces and give a proof of the Cauchy-Schwarz inequality and the Bessel inequality. As an example of application of the Cauchy-Schwarz inequality and the Bessel inequality, we give an estimate for the dimension of an eigenspace of an integral operator. Next we give a proof of Selberg's inequality including the equality conditions following [Furuta]. In Chapter 2 we give selected facts on positive semidefinite matrices with proofs or references. Then
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2

Ameur, Yacin. "Interpolation of Hilbert spaces." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-1753.

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(i) We prove that intermediate Banach spaces A, B with respect to arbitrary Hilbert couples H, K are exact interpolation iff they are exact K-monotonic, i.e. the condition f0∊A and the inequality K(t,g0;K)≤K(t,f0;H), t&gt;0 imply g0∊B and ||g0||B≤||f0||A (K is Peetre's K-functional). It is well-known that this property is implied by the following: for each ρ&gt;1 there exists an operator T : H→K such that Tf0=g0, and K(t,Tf;K)≤ρK(t,f;H), f∊H0+H1, t&gt;0.Verifying the latter property, it suffices to consider the "diagonal" case where H=K is finite-dimensional. In this case, we construct the rel
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3

Ameur, Yacin. "Interpolation of Hilbert spaces /." Uppsala : Matematiska institutionen, Univ. [distributör], 2001. http://publications.uu.se/theses/91-506-1531-9/.

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4

Panayotov, Ivo. "Conjugate gradient in Hilbert spaces." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=82402.

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In this thesis, we examine the Conjugate Gradient algorithm for solving self-adjoint positive definite linear systems in Cn . We generalize the algorithm by proving a convergence result of Conjugate Gradient for self-adjoint positive definite operators in an arbitrary Hilbert space H. Then, we use the Maple software for symbolic manipulation to implement a general version of Conjugate Gradient and to demonstrate, by examples, that the algorithm can be used directly to solve problems in Hilbert spaces other than Cn .
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5

Bahmani, Fatemeh. "Ternary structures in Hilbert spaces." Thesis, Queen Mary, University of London, 2011. http://qmro.qmul.ac.uk/xmlui/handle/123456789/697.

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Ternary structures in Hilbert spaces arose in the study of in nite dimensional manifolds in di erential geometry. In this thesis, we develop a structure theory of Hilbert ternary algebras and Jordan Hilbert triples which are Hilbert spaces equipped with a ternary product. We obtain several new results on the classi - cation of these structures. Some results have been published in [2]. A Hilbert ternary algebra is a real Hilbert space (V; h ; i) equipped with a ternary product [ ; ; ] satisfying h[a; b; x]; yi = hx; [b; a; y]i for a; b; x and y in V . A Jordan Hilbert triple is a real Hilbert s
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6

Das, Tushar. "Kleinian Groups in Hilbert Spaces." Thesis, University of North Texas, 2012. https://digital.library.unt.edu/ark:/67531/metadc149579/.

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The theory of discrete groups acting on finite dimensional Euclidean open balls by hyperbolic isometries was borne around the end of 19th century within the works of Fuchs, Klein and Poincaré. We develop the theory of discrete groups acting by hyperbolic isometries on the open unit ball of an infinite dimensional separable Hilbert space. We present our investigations on the geometry of limit sets at the sphere at infinity with an attempt to highlight the differences between the finite and infinite dimensional theories. We discuss the existence of fixed points of isometries and the classificati
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7

Harris, Terri Joan Mrs. "HILBERT SPACES AND FOURIER SERIES." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/244.

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I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.
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8

Dieuleveut, Aymeric. "Stochastic approximation in Hilbert spaces." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE059/document.

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Le but de l’apprentissage supervisé est d’inférer des relations entre un phénomène que l’on souhaite prédire et des variables « explicatives ». À cette fin, on dispose d’observations de multiples réalisations du phénomène, à partir desquelles on propose une règle de prédiction. L’émergence récente de sources de données à très grande échelle, tant par le nombre d’observations effectuées (en analyse d’image, par exemple) que par le grand nombre de variables explicatives (en génétique), a fait émerger deux difficultés : d’une part, il devient difficile d’éviter l’écueil du sur-apprentissage lorsq
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9

Boralugoda, Sanath Kumara. "Prox-regular functions in Hilbert spaces." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0006/NQ34740.pdf.

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10

Lapinski, Felicia. "Hilbert spaces and the Spectral theorem." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-454412.

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11

Tipton, James Edward. "Reproducing Kernel Hilbert spaces and complex dynamics." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2284.

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Both complex dynamics and the theory of reproducing kernel Hilbert spaces have found widespread application over the last few decades. Although complex dynamics started over a century ago, the gravity of it's importance was only recently realized due to B.B. Mandelbrot's work in the 1980's. B.B. Mandelbrot demonstrated to the world that fractals, which are chaotic patterns containing a high degree of self-similarity, often times serve as better models to nature than conventional smooth models. The theory of reproducing kernel Hilbert spaces also having started over a century ago, didn't pick u
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12

EUSEBI, Anita. "Quantum Cryptography in d-dimensional Hilbert spaces." Doctoral thesis, Università degli Studi di Camerino, 2011. http://hdl.handle.net/11581/401811.

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The topic of this thesis is Quantum Cryptography. Based on the laws of Quantum Mechanics, this allows two parties to share a secure key, by using quantum states to carry classical information. Namely, the Quantum Key Distribution (QKD) process, completed with the classical algorithm One Time Pad, leads to an unconditionally secure cryptosystem. Most QKD protocols, like the famous BB84, are realized on unidirectional quantum channels and have probabilistic character. Recently, a new protocol, named LM05, has been proposed, which works on bidirectional quantum channels and in a deterministic way
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13

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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14

Sprungk, Björn. "Numerical Methods for Bayesian Inference in Hilbert Spaces." Doctoral thesis, Universitätsbibliothek Chemnitz, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-226748.

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Bayesian inference occurs when prior knowledge about uncertain parameters in mathematical models is merged with new observational data related to the model outcome. In this thesis we focus on models given by partial differential equations where the uncertain parameters are coefficient functions belonging to infinite dimensional function spaces. The result of the Bayesian inference is then a well-defined posterior probability measure on a function space describing the updated knowledge about the uncertain coefficient. For decision making and post-processing it is often required to sample or int
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15

VIEIRA, PAULO CESAR MARQUES. "STABILITY FOR DISCRETE LINEAR SYSTEMS IN HILBERT SPACES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1988. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8426@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Este trabalho aborda o problema da estabilidade de sistemas lineares, invariantes no tempo, a tempo discreto, com o espaço de estado sendo um espaço de Hilbert complexo e separável de dimensão infinita. São investigadas condições necessárias e/ou suficientes para quatro conceitos diferentes de estabilidade: estabilidade assintótica uniforme e estabilidade assintótica forte, estabilidade assintótica fraca e estabilidade limitada. Identifica-se e analisa-se as conexões entre os problemas de estabilidade e dois problemas em
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16

Sprungk, Björn. "Numerical Methods for Bayesian Inference in Hilbert Spaces." Doctoral thesis, Technische Universität Chemnitz, 2017. https://monarch.qucosa.de/id/qucosa%3A20754.

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Bayesian inference occurs when prior knowledge about uncertain parameters in mathematical models is merged with new observational data related to the model outcome. In this thesis we focus on models given by partial differential equations where the uncertain parameters are coefficient functions belonging to infinite dimensional function spaces. The result of the Bayesian inference is then a well-defined posterior probability measure on a function space describing the updated knowledge about the uncertain coefficient. For decision making and post-processing it is often required to sample or int
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17

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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18

Sorensen, Julian Karl. "White noise analysis and stochastic evolution equations." Title page, contents and abstract only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phs713.pdf.

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19

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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20

ru, neretin@main mccme rssi. "Groups of Vassalomorphisms and Hilbert Spaces Associated with Trees." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1047.ps.

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21

Struble, Dale William. "Wavelets on manifolds and multiscale reproducing kernel Hilbert spaces." Related electronic resource:, 2007. http://proquest.umi.com/pqdweb?did=1407687581&sid=1&Fmt=2&clientId=3739&RQT=309&VName=PQD.

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22

Saraivanov, Michael S. "Quantum Circuit Synthesis using Group Decomposition and Hilbert Spaces." Thesis, Portland State University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=1542568.

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<p> The exponential nature of Moore's law has inadvertently created huge data storage complexes that are scattered around the world. Data elements are continuously being searched, processed, erased, combined and transferred to other storage units without much regard to power consumption. The need for faster searches and power efficient data processing is becoming a fundamental requirement. Quantum computing may offer an elegant solution to speed and power through the utilization of the natural laws of quantum mechanics. Therefore, minimal cost quantum circuit implementation methodologies are
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23

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 give
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24

McKain, David. "Transference and the Hilbert transform on Banach function spaces." Thesis, University of Edinburgh, 2000. http://hdl.handle.net/1842/12628.

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The thesis begins with a summary of the classical theory of Banach function spaces, including the notions of saturation and associate norms along with the various well-known ideas of completeness. We then go on to establish some rather more "practical" results. In particular we look at the problem of establishing when certain subspaces, such as the simple or continuous functions, are dense in a Banach function space <i>L<sub>p</sub>. </i>We shall see that our intention fails us slightly when considering continuous functions, requiring us to approach that idea of saturation from a slightly diff
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25

Quiggin, Peter Philip. "Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces." Thesis, Lancaster University, 1994. http://eprints.lancs.ac.uk/61962/.

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Pick's theorem states that there exists a function in H1, which is bounded by 1 and takes given values at given points, if and only if a certain matrix is positive. H1 is the space of multipliers of H2 and this theorem has a natural generalisation when H1 is replaced by the space of multipliers of a general reproducing kernel Hilbert space H(K) (where K is the reproducing kernel). J. Agler showed that this generalised theorem is true when H(K) is a certain Sobolev space or the Dirichlet space. This thesis widens Agler's approach to cover reproducing kernel Hilbert spaces in general and derives
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26

Marx, Gregory. "The Complete Pick Property and Reproducing Kernel Hilbert Spaces." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/24783.

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We present two approaches towards a characterization of the complete Pick property. We first discuss the lurking isometry method used in a paper by J.A. Ball, T.T. Trent, and V. Vinnikov. They show that a nondegenerate, positive kernel has the complete Pick property if $1/k$ has one positive square. We also look at the one-point extension approach developed by P. Quiggin which leads to a sufficient and necessary condition for a positive kernel to have the complete Pick property. We conclude by connecting the two characterizations of the complete Pick property.<br>Master of Science
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27

Kaldas, Hany Kamel Halim. "Relativistic Gamow vectors : state vectors for unstable particles /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004300.

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28

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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29

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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30

Giménez, Febrer Pere Joan. "Matrix completion with prior information in reproducing kernel Hilbert spaces." Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/671718.

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In matrix completion, the objective is to recover an unknown matrix from a small subset of observed entries. Most successful methods for recovering the unknown entries are based on the assumption that the unknown full matrix has low rank. By having low rank, each of its entries are obtained as a function of a small number of coefficients which can be accurately estimated provided that there are enough available observations. Hence, in low-rank matrix completion the estimate is given by the matrix of minimum rank that fits the observed entries. Besides low rankness, the unknown matrix might
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31

Sinha, Suddhasattwa. "Coherent control of dipolar coupled spins in large Hilbert spaces." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/41278.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2006.<br>Includes bibliographical references (p. 101-106).<br>Controlling the dynamics of a dipolar-coupled spin system is critical to the development of solid-state spin-based quantum information processors. Such control remains challenging, as every spin is coupled to a large number of surrounding spins. In this thesis, we primarily focus on developing coherent control techniques for such large spin systems. We start by experimentally simulating spin squeezing using a liquid-state NMR quantum in
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32

Thompson, Kinney. "Frames for Hilbert spaces and an application to signal processing." VCU Scholars Compass, 2012. http://scholarscompass.vcu.edu/etd/2735.

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The goal of this paper will be to study how frame theory is applied within the field of signal processing. A frame is a redundant (i.e. not linearly independent) coordinate system for a vector space that satisfies a certain Parseval-type norm inequality. Frames provide a means for transmitting data and, when a certain about of loss is anticipated, their redundancy allows for better signal reconstruction. We will start with the basics of frame theory, give examples of frames and an application that illustrates how this redundancy can be exploited to achieve better signal reconstruction. We also
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33

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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34

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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35

Becker, Tanja. "Moduli spaces of (G,h)-constellations." Nantes, 2011. http://www.theses.fr/2011NANT2073.

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Nous construisons l'espace de modules M(X) des (G; h)constellations stables sur X pour un groupe réductif G qui agit sur un schéma ane X sur C et pour une fonction de Hilbert h: IrrG ! N0. Cet espace de modules est une généralisation commune du schéma de Hilbert invariant d'après Alexeev et Brion [AB05] et de l'espace de modules des Gconstellations stables pour un groupe ni G introduit par Craw et Ishii [CI04]. Notre construction d'un morphisme M(X) ! X//G fait de cet espace de modules un candidat pour une résolution des singularités du quotient X//G. De plus, nous déterminons le schéma de Hil
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36

Van, Tuyl Adam Leonard. "Sets of points in multi-projective spaces and their Hilbert function." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63465.pdf.

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37

Wickramasekara, Sujeewa. "Differentiable representations of finite dimensional lie groups in rigged Hilbert spaces /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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38

Wickramasekara, Sujeewa, and sujeewa@physics utexas edu. "Symmetry Representations in the Rigged Hilbert Space Formulation of." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi993.ps.

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39

Allen, Cristian Gerardo. "A Classification of the Homogeneity of Countable Products of Subsets of Real Numbers." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011753/.

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Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And finally we show that for a Borel subset X of real numbers the product is CDH iff X is a G-delta zero-d
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40

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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41

Kotsakis, Christophoros. "Multiresolution aspects of linear approximation methods in Hilbert spaces using gridded data." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0016/NQ54794.pdf.

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42

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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43

Maruhn, Jan Hendrik. "An augmented Lagrangian algorithm for optimization with equality constraints in Hilbert spaces." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/32098.

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Since augmented Lagrangian methods were introduced by Powell and Hestenes, this class of methods has been investigated very intensively. While the finite dimensional case has been treated in a satisfactory manner, the infinite dimensional case is studied much less. The general approach to solve an infinite dimensional optimization problem subject to equality constraints is as follows: First one proves convergence for a basic algorithm in the Hilbert space setting. Then one discretizes the given spaces and operators in order to make numerical computations possible. Finally, one constructs a di
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44

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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Chui, Nelson Loong Chik. "Subspace methods and informative experiments for system identification." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298794.

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46

Santiago, Landerson Bezerra. "O nÃcleo do calor em uma variedade riemanniana." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5674.

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Em uma variedade riemanniana conexa e compacta introduziremos o conceito de espectro do operador laplaciano. Utilizando a existÃncia e a unicidade do nÃcleo do calor em uma variedade riemanniana,provaremos o teorema de decomposiÃÃo de Hodge. Este teorema afirma que o espaÃo de Hilbert L2(M, g) se decompÃe em uma soma direta de subespaÃos de dimensÃo finita, onde cada subespaÃo à o auto-espaÃo associado a um autovalor do laplaciano. AlÃm disso, os autovalores formam uma sequÃncia nÃo-negativa que acumula somente no infinito. Em seguida iniciaremos a construÃÃo do nÃcleo do calor e, por fim, mos
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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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Montgomery, Jason W. "Condition-dependent Hilbert Spaces for Steepest Descent and Application to the Tricomi Equation." Thesis, University of North Texas, 2014. https://digital.library.unt.edu/ark:/67531/metadc699977/.

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A steepest descent method is constructed for the general setting of a linear differential equation paired with uniqueness-inducing conditions which might yield a generally overdetermined system. The method differs from traditional steepest descent methods by considering the conditions when defining the corresponding Sobolev space. The descent method converges to the unique solution to the differential equation so that change in condition values is minimal. The system has a solution if and only if the first iteration of steepest descent satisfies the system. The finite analogue of the descent m
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Paiva, António R. C. "Reproducing kernel Hilbert spaces for point processes, with applications to neural activity analysis." [Gainesville, Fla.] : University of Florida, 2008. http://purl.fcla.edu/fcla/etd/UFE0022471.

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Bhujwalla, Yusuf. "Nonlinear System Identification with Kernels : Applications of Derivatives in Reproducing Kernel Hilbert Spaces." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0315/document.

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Cette thèse se concentrera exclusivement sur l’application de méthodes non paramétriques basées sur le noyau à des problèmes d’identification non-linéaires. Comme pour les autres méthodes non-linéaires, deux questions clés dans l’identification basée sur le noyau sont les questions de comment définir un modèle non-linéaire (sélection du noyau) et comment ajuster la complexité du modèle (régularisation). La contribution principale de cette thèse est la présentation et l’étude de deux critères d’optimisation (un existant dans la littérature et une nouvelle proposition) pou
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