Ii Fourier Analysis Self Adjointness
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Ii Fourier Analysis Self Adjointness
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Author : Michael Reed
language : en
Publisher: Elsevier
Release Date : 1975
Ii Fourier Analysis Self Adjointness written by Michael Reed and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Band 2.
Methods Of Modern Mathematical Physics Ii Fourier Analysis Self Adjointness
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Author : Michael Reed
language : en
Publisher:
Release Date : 1972
Methods Of Modern Mathematical Physics Ii Fourier Analysis Self Adjointness written by Michael Reed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Methods Of Modern Mathematical Physics Ii Fourier Analysis Self Adjointness
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Author : Michael Reed
language : en
Publisher:
Release Date : 1972
Methods Of Modern Mathematical Physics Ii Fourier Analysis Self Adjointness written by Michael Reed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations
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Author : Johannes Sjöstrand
language : en
Publisher: Springer
Release Date : 2019-05-17
Non Self Adjoint Differential Operators Spectral Asymptotics And Random Perturbations written by Johannes Sjöstrand and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-17 with Mathematics categories.
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.
The Method Of Rigged Spaces In Singular Perturbation Theory Of Self Adjoint Operators
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Author : Volodymyr Koshmanenko
language : en
Publisher: Birkhäuser
Release Date : 2016-07-08
The Method Of Rigged Spaces In Singular Perturbation Theory Of Self Adjoint Operators written by Volodymyr Koshmanenko and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-08 with Mathematics categories.
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.
Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians
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Author : Matteo Gallone
language : en
Publisher: Springer Nature
Release Date : 2023-04-04
Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians written by Matteo Gallone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-04 with Science categories.
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.
Methods Of Modern Mathematical Physics Functional Analysis
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Author : Michael Reed
language : en
Publisher: Gulf Professional Publishing
Release Date : 1980
Methods Of Modern Mathematical Physics Functional Analysis written by Michael Reed and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Functional analysis categories.
"This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." --Publisher description.
Introduction To The Mathematical Structure Of Quantum Mechanics An A Short Course For Mathematicians
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Author : Franco Strocchi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-11-17
Introduction To The Mathematical Structure Of Quantum Mechanics An A Short Course For Mathematicians written by Franco Strocchi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-17 with Science categories.
This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac-Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C--algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems.For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich-Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.
Progress In Analysis Proceedings Of The 3rd Isaac Congress In 2 Volumes
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Author : Heinrich G W Begehr
language : en
Publisher: World Scientific
Release Date : 2003-08-04
Progress In Analysis Proceedings Of The 3rd Isaac Congress In 2 Volumes written by Heinrich G W Begehr and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-04 with Mathematics categories.
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Geometric Aspects Of Partial Differential Equations
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Author : Krzysztof Wojciechowski
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Geometric Aspects Of Partial Differential Equations written by Krzysztof Wojciechowski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This collection of papers by leading researchers gives a broad picture of current research directions in geometric aspects of partial differential equations. Based on lectures presented at a Minisymposium on Spectral Invariants - Heat Equation Approach, held in September 1998 at Roskilde University in Denmark, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are new index theorems as well as new calculations of the eta-invariant, of the spectral flow, of the Maslov index, of Seiberg-Witten monopoles, heat kernels, determinants, non-commutative residues, and of the Ray-Singer torsion. New types of boundary value problems for operators of Dirac type and generalizations to manifolds with cuspidal ends, to non-compact and to infinite-dimensional manifolds are also discussed. Throughout the book, the use of advanced analysis methods for gaining geometric insight emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on geometric aspects of partial differential equations and spectral invariants.