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Spectral theory of self-adjoint operators in Huilbert space.
Authors: ---
ISBN: 9027721793 9401090092 9400945868 Year: 1987 Publisher: Dordrecht ; Boston, MA : D. Reidel,


Book
Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations
Author:
ISBN: 3030108198 303010818X Year: 2019 Publisher: Cham : Springer International Publishing : Imprint: Birkhäuser,

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Abstract

The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago. In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book. Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.

Infinite Groups: Geometric, Combinatorial and Dynamical Aspects
Authors: --- --- ---
ISBN: 1280608889 9786610608881 3764374470 3764374462 9783764374464 9783764374471 Year: 2005 Publisher: Basel : Birkhäuser Basel : Imprint: Birkhäuser,

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This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. This interdisciplinary approach makes the book interesting to a large mathematical audience. Contributors: G. Baumslag A.V. Borovik T. Delzant W. Dicks E. Formanek R. Grigorchuk M. Gromov P. de la Harpe A. Lubotzky W. Lück A.G. Myasnikov C. Pache G. Pisier A. Shalev S. Sidki E. Zelmanov.


Book
Unbounded self-adjoint operators on Hilbert space
Authors: ---
ISBN: 1282059165 9786613799005 9400747535 9400747527 9400797419 9789400747524 Year: 2012 Publisher: Dordrecht ; Heidelberg ; New York ; London : Springer,

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The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem). Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises.

Methods of modern mathematical physics.
Authors: ---
ISBN: 0125850018 0125850026 0125850034 0125850042 0323155006 1299472656 9780125850049 9780125850025 9780125850018 9780125850032 Year: 1975 Volume: 3 Publisher: New York : Academic Press,

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Keywords

Mathematical physics --- Physique mathématique --- 517.98 --- Physical mathematics --- Physics --- Functional analysis and operator theory --- Mathematics --- Mathematical physics. --- 517.98 Functional analysis and operator theory --- Physique mathématique --- 517.983 --- 517.983 Linear operators. Linear operator equations --- Linear operators. Linear operator equations --- 517.44 --- #WWIS:ANAL --- 517.44 Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Integral transforms. Operational calculus. Laplace transforms. Fourier integral. Fourier transforms. Convolutions --- Operator theory --- Harmonic analysis. Fourier analysis --- Analyse fonctionnelle --- Functional analysis --- Fourier, Analyse de --- Functional analysis. --- Schroedinger operator --- Perturbation theory in quantum mechanics --- Operators(Non Self Adjoint-/Spectral Analysis) --- Spectral analysis of non self adjoint operators --- Operators(Self Adjoint-/Spectral Analysis) --- Spectral analysis of self adjoint operators --- Fourier transform --- Functional analysis in physics --- Operator extensions(Symmetric-) --- Semi groups of operators --- Operators(Self Adjoint-) --- Scattering in quantum field theory --- Scattering of non linear waves --- Scattering in quantum mechanics --- Light scattering --- Sound scattering --- Lax-Philips method in scattering theory --- Scattering theory --- Schroedinger operator in scattering theory --- Operateurs hilbertiens

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