Microlocal Analysis

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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.

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 Most of the results and almost all the proofs are as yet unpublished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 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.

Microlocal Analysis Sharp Spectral Asymptotics And Applications Iii

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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-12

Microlocal Analysis Sharp Spectral Asymptotics And Applications Iii written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Mathematics categories.

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3.

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.

Microlocal Analysis Sharp Spectral Asymptotics And Applications Iv

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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-11

Microlocal Analysis Sharp Spectral Asymptotics And Applications Iv written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Mathematics categories.

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II and III are applied to the Schrödinger and Dirac operators in non-smooth settings and in higher dimensions.

New Trends In Microlocal Analysis

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Author : J.-M. Bony
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

New Trends In Microlocal Analysis written by J.-M. Bony 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 2012-12-06 with Mathematics categories.

Microlocal analysis began around 1970 when Mikio Sato, along with coauthors Masaki Kashiwara and Takahiro Kawai, wrote a decisive article on the structure of pseudodifferential equations, thus laying the foundation of D-modules and the singular spectrums of hyperfunctions. The key idea is the analysis of problems on the phase space, i.e., the cotangent bundle of the base space. Microlocal analysis is an active area of mathematical research that has been applied to many fields such as real and complex analysis, representation theory, topology, number theory, and mathematical physics. This volume contains the presentations given at a seminar jointly organized by the Japan Society for the Promotion of Science and Centre National des Recherches Scientifiques entitled New Trends in Microlocal Analysis. The book is divided into three parts: partial differential equations and mathematical analysis, mathematical physics, and algebraic analysis - D-modules and sheave theory. The large variety of new research that is covered will prove invaluable to students and researchers alike.

Microlocal Analysis And Spectral Theory

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Author : Luigi Rodino
language : en
Publisher: Springer Science & Business Media
Release Date : 1997

Microlocal Analysis And Spectral Theory written by Luigi Rodino 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 1997 with Mathematics categories.

There has been considerable progress in the field of microlocal analysis. In a broad sense the subject is the modern version of the classical Fourier technique for solving partial differential equations, with the localization process taking account of dual variables. The tools of pseudo-differential operators, wave-front sets and Fourier integral operators have now conferred a mature form on the theory of linear partial differential operators in the frame of Schwartz distributions or other generalized functions. At the same time, microlocal analysis has assumed an important role as an independent part of analysis, with other applications throughout mathematics and physics, one major theme being spectral theory for the Schrodinger equation in quantum mechanics.

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.

Microlocal Analysis Sharp Spectral Asymptotics And Applications Ii

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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-11

Microlocal Analysis Sharp Spectral Asymptotics And Applications Ii written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Mathematics categories.

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the local spectral asymptotics of Volume I in the regular part of the domain are combined with variational estimates in the vicinity of singularities, and global asymptotics are derived in the general form. They are then applied to multiple cases and asymptotics with respect to a spectral parameter. Finally, cases in which only general methods but not the results can be applied (non-standard asymptotics) are studied.