Around Microlocal Analysis
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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 Most of the results and almost all the proofs are as yet unpublished
Microlocal Analysis For Differential Operators
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Author : Alain Grigis
language : en
Publisher: Cambridge University Press
Release Date : 1994-03-03
Microlocal Analysis For Differential Operators written by Alain Grigis 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 1994-03-03 with Mathematics categories.
This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
An Introduction To Semiclassical And Microlocal Analysis
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Author : André Bach
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-02
An Introduction To Semiclassical And Microlocal Analysis written by André Bach 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 2002-01-02 with Mathematics categories.
This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Semiclassical Analysis
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Author : Maciej Zworski
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Semiclassical Analysis written by Maciej Zworski 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 2012 with Mathematics categories.
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Singularities Of Integrals
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Author : Frédéric Pham
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-22
Singularities Of Integrals written by Frédéric Pham 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 2011-04-22 with Mathematics categories.
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
Asymptotic Analysis In General Relativity
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Author : Thierry Daudé
language : en
Publisher: Cambridge University Press
Release Date : 2018-01-11
Asymptotic Analysis In General Relativity written by Thierry Daudé 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 2018-01-11 with Mathematics categories.
Introduction to modern methods for classical and quantum fields in general relativity / Thierry Daudé, Dietrich Häfner, and Jean-Philippe Nicolas -- Geometry of black hole spacetimes / Lars Andersson, Thomas B. Ackdahl, and Pieter Blue -- An introduction to Quantum Field Theory on curved space-times / Christian Gerard -- A minicourse on microlocal analysis for wave propagation / Andras Vasy -- An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity / Sean N. Curry and A. Rod Gover
An Introduction To Semiclassical And Microlocal Analysis
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Author : André Bach
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
An Introduction To Semiclassical And Microlocal Analysis written by André Bach 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 2013-03-14 with Mathematics categories.
The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy). They are mainly addressed to nonspecialists in the subject, and their purpose is to present in a pedagogical way most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard Coo pseudodifferential calculus and the analytic microlocal analysis are developed, in a context that remains intentionally global so that only the relevant difficulties of the theory are encountered. The main original ity lies in the fact that we derive all the main features of analytic microlocal analysis from a single a priori estimate, which turns out to be elementary once the Coo pseudodifferential calculus is established. Various detailed exercises are given at the end of the main chapters, most of them being easily solvable by students. Besides illustrating the main results of the lecture, their aim is also to introduce the reader to various further developments of the theory, such as the functional calculus of pseudodifferential operators, properties of the analytic wave front set, Gevrey classes, the use of coherent states, the notion of semiclassical measures, WKB constructions. Applications to the study of the Schrodinger operator are also discussed in the text, so that they may help the understanding of new notions or general results where they appear by replacing them in the context of quantum mechanics.
Geometric Scattering Theory
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Author : Richard B. Melrose
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-28
Geometric Scattering Theory written by Richard B. Melrose 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 1995-07-28 with Mathematics categories.
These lecture notes are intended as a non-technical overview of scattering theory.
Fundamentals Of Algebraic Microlocal Analysis
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Author : Goro Kato
language : en
Publisher: CRC Press
Release Date : 1999-01-08
Fundamentals Of Algebraic Microlocal Analysis written by Goro Kato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-08 with Mathematics categories.
"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."
Microlocal Analysis And Precise Spectral Asymptotics
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Author : Victor Ivrii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
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 2013-03-14 with Mathematics categories.
The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; moreover, it is very important for the general theory of partial differential operators. I started working in this domain in 1979 after R. Seeley found a remainder estimate of the same order as the then hypothetical second term for the Laplacian in domains with boundary, and M. Shubin and B. M. Levitan suggested that I should try to prove Weyl's conjecture. During the past fifteen years I have not left the topic, although I had such intentions in 1985 when the methods I invented seemed to fai! to provide furt her progress and only a couple of not very exciting problems remained to be solved. However, at that time I made the step toward local semiclassical spectral asymptotics and rescaling, and new horizons opened.