Fourier Integral Operators

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Fourier Integral Operators

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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-11-29

Fourier Integral Operators written by J.J. Duistermaat 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 1995-11-29 with Mathematics categories.

This volume is a useful introduction to the subject of Fourier Integral Operators and is based on the author’s classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, rep. WKB-methods.

Fourier Integral Operators

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Author : Johannes Jisse Duistermaat
language : en
Publisher:
Release Date : 1971

Fourier Integral Operators written by Johannes Jisse Duistermaat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.

The Analysis Of Linear Partial Differential Operators Iv

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Author : Lars Hörmander
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-28

The Analysis Of Linear Partial Differential Operators Iv written by Lars Hörmander 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 2009-04-28 with Mathematics categories.

From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987 "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987 Honours awarded to Lars Hörmander: Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006

Fourier Integral Operators

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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-03

Fourier Integral Operators written by J.J. Duistermaat 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 2010-11-03 with Mathematics categories.

This volume is a useful introduction to the subject of Fourier Integral Operators and is based on the author’s classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, rep. WKB-methods.

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.

Pseudodifferential And Singular Integral Operators

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Author : Helmut Abels
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23

Pseudodifferential And Singular Integral Operators written by Helmut Abels and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.

Fourier Integral Operators And Partial Differential Equations

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Author : J. Chazarain
language : en
Publisher:
Release Date : 2014-01-15

Fourier Integral Operators And Partial Differential Equations written by J. Chazarain and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Fourier Integral Operators

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Author : J. J. Duistermaat
language : en
Publisher:
Release Date : 1972

Fourier Integral Operators written by J. J. Duistermaat 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.

Mathematics Past And Present Fourier Integral Operators

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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-18

Mathematics Past And Present Fourier Integral Operators written by J.J. Duistermaat 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 1994-02-18 with Mathematics categories.

What is the true mark of inspiration? Ideally it may mean the originality, freshness and enthusiasm of a new breakthrough in mathematical thought. The reader will feel this inspiration in all four seminal papers by Duistermaat, Guillemin and Hörmander presented here for the first time ever in one volume. However, as time goes by, the price researchers have to pay is to sacrifice simplicity for the sake of a higher degree of abstraction. Thus the original idea will only be a foundation on which more and more abstract theories are being built. It is the unique feature of this book to combine the basic motivations and ideas of the early sources with knowledgeable and lucid expositions on the present state of Fourier Integral Operators, thus bridging the gap between the past and present. A handy and useful introduction that will serve novices in this field and working mathematicians equally well.