Spectral Theory And Asymptotics Of Differential Equations

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Spectral Theory And Asymptotics Of Differential Equations

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Author :
language : en
Publisher: Elsevier
Release Date : 2011-09-21

Spectral Theory And Asymptotics Of Differential Equations written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-21 with Mathematics categories.

Spectral Theory and Asymptotics of Differential Equations

Spectral Theory And Asymptotics Of Differential Equations

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Author : Eduardus Marie de Jager
language : en
Publisher:
Release Date : 1974

Spectral Theory And Asymptotics Of Differential Equations written by Eduardus Marie de Jager and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.

Microlocal Analysis And Precise Spectral Asymptotics

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Author : Victor Ivrii
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-05-20

Microlocal Analysis And Precise Spectral Asymptotics written by Victor Ivrii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-20 with Mathematics categories.

This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should be mentioned as an easy as to use and very powerful tool. Many theorems, considered before as independent and difficult, now are just special cases of easy corollaries of the theorems proved in the book. Most of the results and almost all the proofs are as yet unpublished

Spectral Theory And Asymptotics Of Differential Equations

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Author : Eduardus Marie de Jager
language : en
Publisher:
Release Date : 1974

Spectral Theory And Asymptotics Of Differential Equations written by Eduardus Marie de Jager and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Asymptotic expansions categories.

Spectral Theory And Asymptotics Of Differential Equations

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Author :
language : en
Publisher:
Release Date : 1974

Spectral Theory And Asymptotics Of Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.

Spectral Theory And Asymptotics Of Differential Equations Proceedings Of The Scheveningen Conference On Differential Equations The Netherlands September 3 7 1973

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Author : E. M. de Jager
language : en
Publisher:
Release Date : 1974

Spectral Theory And Asymptotics Of Differential Equations Proceedings Of The Scheveningen Conference On Differential Equations The Netherlands September 3 7 1973 written by E. M. de Jager and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Asymptotic Expansions Congresses categories.

Spectral Theory And Asymptotics Of Differential Equations

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Author : Eduardus M. de Jager
language : en
Publisher:
Release Date : 1974

Spectral Theory And Asymptotics Of Differential Equations written by Eduardus M. de Jager and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Asymptotes categories.

Partial Differential Equations Vii

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Author : M.A. Shubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Partial Differential Equations Vii written by M.A. Shubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

§18 Operators with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . 186 18. 1. General Definitions. Essential Self-Adjointness . . . . . . . . . . . . 186 18. 2. General Properties of the Spectrum and Eigenfunctions . . . . 188 18. 3. The Spectrum of the One-Dimensional Schrödinger Operator with an Almost Periodic Potential . . . . . . . . . . . . . . 192 18. 4. The Density of States of an Operator with Almost Periodic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 18. 5. Interpretation of the Density of States with the Aid of von Neumann Aigebras and Its Properties . . . . . . . . . . . . . . 199 §19 Operators with Random Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 206 19. 1. Translation Homogeneous Random Fields . . . . . . . . . . . . . . . . . 207 19. 2. Random DifferentialOperators . . . . . . . . . . . . . . . . . . . . . . . . . . 212 19. 3. Essential Self-Adjointness and Spectra . . . . . . . . . . . . . . . . . . . 214 19. 4. Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 19. 5. The Character of the Spectrum. Anderson Localization 220 §20 Non-Self-Adjoint Differential Operators that Are Close to Self-Adjoint Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 1. Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 20. 2. Basic Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 20. 3. Completeness Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 20. 4. Expansion and Summability Theorems. Asymptotic Behaviour of the Spectrum . . . . . . . . . . . . . . . . . . . 228 20.5. Application to DifferentialOperators . . . . . . . . . . . . . . . . . . . . . 230 Comments on the Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Author Index 262 Subject Index 265 Preface The spectral theory of operators in a finite-dimensional space first appeared in connection with the description of the frequencies of small vibrations of me chanical systems (see Arnol'd et al. 1985). When the vibrations of astring are considered, there arises a simple eigenvalue problem for a differential opera tor. In the case of a homogeneous string it suffices to use the classical theory 6 Preface of Fourier series.

Differential Operators And Spectral Theory

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Author : M. Sh Birman
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Differential Operators And Spectral Theory written by M. Sh Birman 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 volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman. The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrodinger operator, which is within Birman's current scope of interests and recently has been studied extensively. Included is a detailed survey of his mathematical work and an updated list of his publications.This book is aimed at graduate students and specialists in the above-mentioned branches of mathematics and theoretical physicists. The biographical section will be of interest to readers concerned with the scientific activities of Birman and the history of those branches of analysis and spectral theory where his contributions were important and often decisive. Features: The first detailed survey of Birman's mathematical work; includes an updated bibliography. New material on the history of some branches of analysis. Prominent authors: Lieb, Agmon, Deift, Simon, Ladyzhenskaya, and others. All original works, containing new results in fields of great current interest.

Spectral Asymptotics In The Semi Classical Limit

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Author : Mouez Dimassi
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-16

Spectral Asymptotics In The Semi Classical Limit written by Mouez Dimassi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-16 with Mathematics categories.

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.