Introduction To Pseudodifferential And Fourier
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Introduction To Pseudodifferential And Fourier Integral Operators
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Author : Jean-François Treves
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Introduction To Pseudodifferential And Fourier Integral Operators written by Jean-François Treves 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 2013-12-11 with Mathematics categories.
I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying these operators is pragmatic, much attention has been paid to explaining their handling and to giving examples of their use. Thus the theoretical chapters usually begin with a section in which the construction of special solutions of linear partial differential equations is carried out, constructions from which the subsequent theory has emerged and which continue to motivate it: parametrices of elliptic equations in Chapter I (introducing pseudodifferen tial operators of type 1, 0, which here are called standard), of hypoelliptic equations in Chapter IV (devoted to pseudodifferential operators of type p, 8), fundamental solutions of strongly hyperbolic Cauchy problems in Chap ter VI (which introduces, from a "naive" standpoint, Fourier integral operators), and of certain nonhyperbolic forward Cauchy problems in Chapter X (Fourier integral operators with complex phase). Several chapters-II, III, IX, XI, and XII-are devoted entirely to applications. Chapter II provides all the facts about pseudodifferential operators needed in the proof of the Atiyah-Singer index theorem, then goes on to present part of the results of A. Calderon on uniqueness in the Cauchy problem, and ends with a new proof (due to J. J. Kohn) of the celebrated sum-of-squares theorem of L. Hormander, a proof that beautifully demon strates the advantages of using pseudodifferential operators.
Introduction To Pseudodifferential And Fourier Integral Operators Volume 2
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Author : François Trèves
language : en
Publisher: Springer Science & Business Media
Release Date : 1980
Introduction To Pseudodifferential And Fourier Integral Operators Volume 2 written by François Trèves 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 1980 with Fourier integral operators categories.
Introduction To Pseudodifferential And Fourier Integral Operators
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Author : François Treves
language : en
Publisher:
Release Date : 1980
Introduction To Pseudodifferential And Fourier Integral Operators written by François Treves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Introduction To Pseudodifferential And Fourier Integral Operators
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Author : Francois Treves
language : en
Publisher: Springer
Release Date : 1980-11-30
Introduction To Pseudodifferential And Fourier Integral Operators written by Francois Treves and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-11-30 with Mathematics categories.
I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying these operators is pragmatic, much attention has been paid to explaining their handling and to giving examples of their use. Thus the theoretical chapters usually begin with a section in which the construction of special solutions of linear partial differential equations is carried out, constructions from which the subsequent theory has emerged and which continue to motivate it: parametrices of elliptic equations in Chapter I (introducing pseudodifferen tial operators of type 1, 0, which here are called standard), of hypoelliptic equations in Chapter IV (devoted to pseudodifferential operators of type p, 8), fundamental solutions of strongly hyperbolic Cauchy problems in Chap ter VI (which introduces, from a "naive" standpoint, Fourier integral operators), and of certain nonhyperbolic forward Cauchy problems in Chapter X (Fourier integral operators with complex phase). Several chapters-II, III, IX, XI, and XII-are devoted entirely to applications. Chapter II provides all the facts about pseudodifferential operators needed in the proof of the Atiyah-Singer index theorem, then goes on to present part of the results of A. Calderon on uniqueness in the Cauchy problem, and ends with a new proof (due to J. J. Kohn) of the celebrated sum-of-squares theorem of L. Hormander, a proof that beautifully demon strates the advantages of using pseudodifferential operators.
Introduction To Pseudo Differential Operators An 3rd Edition
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Author : Man-wah Wong
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-03-11
Introduction To Pseudo Differential Operators An 3rd Edition written by Man-wah Wong 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 2014-03-11 with Mathematics categories.
The aim of this third edition is to give an accessible and essentially self-contained account of pseudo-differential operators based on the previous edition. New chapters notwithstanding, the elementary and detailed style of earlier editions is maintained in order to appeal to the largest possible group of readers. The focus of this book is on the global theory of elliptic pseudo-differential operators on Lp(Rn).The main prerequisite for a complete understanding of the book is a basic course in functional analysis up to the level of compact operators. It is an ideal introduction for graduate students in mathematics and mathematicians who aspire to do research in pseudo-differential operators and related topics.
Introduction To Pseudodifferential And Fourier Integral Operators
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Author : François Treves
language : en
Publisher:
Release Date : 1982
Introduction To Pseudodifferential And Fourier Integral Operators written by François Treves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Introduction To Pseudodifferential And Fourier
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Author : Francois Treves
language : en
Publisher:
Release Date : 1980
Introduction To Pseudodifferential And Fourier written by Francois Treves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
An Introduction To Pseudodifferential And Fourier Integral Operators
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Author : Francois Treves
language : en
Publisher:
Release Date : 1973
An Introduction To Pseudodifferential And Fourier Integral Operators written by Francois Treves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Introduction To Pseudodifferential And Fourier Integral Operators Volume 2
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Author : Jean-François Treves
language : en
Publisher: Springer
Release Date : 1980-11-30
Introduction To Pseudodifferential And Fourier Integral Operators Volume 2 written by Jean-François Treves and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-11-30 with Mathematics categories.
Elementary Introduction To The Theory Of Pseudodifferential Operators
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Author : Xavier Saint Raymond
language : en
Publisher: Routledge
Release Date : 2018-02-06
Elementary Introduction To The Theory Of Pseudodifferential Operators written by Xavier Saint Raymond and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-06 with Mathematics categories.
In the 19th century, the Fourier transformation was introduced to study various problems of partial differential equations. Since 1960, this old tool has been developed into a well-organized theory called microlocal analysis that is based on the concept of the pseudo-differential operator. This book provides the fundamental knowledge non-specialists need in order to use microlocal analysis. It is strictly mathematical in the sense that it contains precise definitions, statements of theorems and complete proofs, and follows the usual method of pure mathematics. The book explains the origin of the theory (i.e., Fourier transformation), presents an elementary construcion of distribution theory, and features a careful exposition of standard pseudodifferential theory. Exercises, historical notes, and bibliographical references are included to round out this essential book for mathematics students; engineers, physicists, and mathematicians who use partial differential equations; and advanced mathematics instructors.