Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 72 for “"Hilbert spaces"”.
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HILBERT SPACES AND FOURIER SERIES
<p>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 …
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Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces
… 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 …
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Geometrical and Martingale characterizations of UMD and Hilbert spaces
… space with norm $\vert \cdot \vert$. Then X is a Hilbert space if and only if $E\vert x + Y\vert \geq 1$ for all x $\in$ X and all X-valued Bochner integrable functions Y on the Lebesgue unit interval satisfying EY = 0 and $\vert Y\vert \geq$ 1 a.e. This leads to a simple proof of the …
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The Complete Pick Property and Reproducing Kernel Hilbert Spaces
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 …
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The Structure of Operator Systems on Finite-Dimensional Hilbert Spaces
The purpose of this thesis is to describe in detail the structure of arbitrary operator systems S B(H), where H is assumed to be of finite dimension, using Arveson's non-commutative Choquet theory, and to determine the C* -envelope of S in certain special cases of interest. Arveson classifies these …
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Coherent control of dipolar coupled spins in large Hilbert spaces
… network to a much smaller subspace of the system Hilbert space which allows us to significantly extend the phase coherence times for selected states. Finally, we demonstrate the sensitivity of highly correlated multiple-quantum states to the presence of rare spin defects in a solid-state spin …
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Extension of Shor's period-finding algorithm to infinite dimensional Hilbert spaces
… hidden subspace of a function with domain a real Hilbert space. After reviewing the framework of quantum mechanics, we demonstrate how these principles can be used to develop algorithms which operate on a quantum computing device. We present a self-contained account of white noise analysis, …
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Theory of reproducing kernels for Hilbert spaces of vector valued functions
… of view for the study of an important class of Hilbert spaces of real or complex valued functions and for the application of the methods of Hilbert space theory to different problems in the theory of partial differential equations. With a view to applications to systems of such equations the …
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Kernels of adjoints of composition operators on Hilbert spaces of analytic functions
… operator and its kernel in weighted Hardy spaces, in particular, the classical Hardy, Bergman, and Dirichlet spaces. In 2006, Cowen and Gallardo-Gutiérrez laid the groundwork for an explicit formula for the adjoint of a composition operator with rational symbol acting on the Hardy space, …
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Applications of metrics over Tikonov semifields and fixed points in Hilbert spaces
<p>"For Non expansive mappings on locally convex spaces, sufficient conditions are given for the set of fixed points to be a Non expansive retract. Also, sufficient conditions are given for certain semigroups of asymptotically Non expansive mappings to have a common fixed point.</p> <p>Several …
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On non-stationary Wishart matrices and functional Gaussian approximations in Hilbert spaces
… theorems for approximations by non-degenerate Hilbert-valued Gaussian random elements, as well as fourth moment bounds for approximating sequences with finite chaos expansion. We apply our results to the Brownian approximation of Poisson processes in Besov-Liouville spaces and also derive a …
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An augmented Lagrangian algorithm for optimization with equality constraints in Hilbert spaces
… 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 discretized version of the infinite dimensional method and tries to transfer the convergence …
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The use of spin-pure and non-orthogonal Hilbert spaces in Full Configuration Interaction Quantum Monte-Carlo
… in the size and internal connectivity of the Hilbert space considered, with associated reductions in the computational cost involved, as well as permitting exclusion of the natural ground state to extract a se- ries of excited states of the system. As all converged solutions are ˆ …
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Minimax in the theory of operators on Hilbert spaces and Clarkson-McCarthy estimates for lq (Sp) spaces of operators in the Schatten ideals
… 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 …
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On the Necessity of Complex Numbers in Quantum Mechanics
… representation in real, complex or quaternionic Hilbert spaces as established by Solèr’s theorem (1995) closing a long standing problem that can be traced back to von Neumann’s mathematical formulation of quantum mechanics. However up to now there are no examples of quantum systems described in …
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Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Cayley numbers
… Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite …
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The Segal-Bargmann transform on inductive limits of compact symmetric spaces
… transform on the direct limit of the Hilbert spaces $\{L^2(M_n)^{K_n}\}_n$ where $\{M_n = U_n/K_n\}_n$ is a propagating sequence of symmetric spaces of compact type with the assumption that $U_n$ is simply connected for each $n$. This map is obtained by taking the direct limit of the …
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Applications in Fixed Point Theory
… due to Browder, Göhde, and Kirk involving Hilbert spaces and nonexpansive mappings. Several applications of Banach's contraction principle are made. Some of these applications involve obtaining new metrics on a space, forcing a continuous map to have a fixed point, and using conditions on …
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