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Fourier Integral Operators


Fourier Integral Operators
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Fourier Integral Operators


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.




Introduction To Pseudodifferential And Fourier Integral Operators Volume 2


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.




Mathematics Past And Present Fourier Integral Operators


Mathematics Past And Present Fourier Integral Operators
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Author : Jochen Brüning
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Mathematics Past And Present Fourier Integral Operators written by Jochen Brüning 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.


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.



Introduction To Pseudodifferential And Fourier Integral Operators


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.



Fourier Integral Operators And Partial Differential Equations


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


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.



Fourier Integral Operators


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.




Fourier Integral Operators And Partial Differential Equations


Fourier Integral Operators And Partial Differential Equations
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Author : J. Chazarain
language : en
Publisher: Springer
Release Date : 2006-11-14

Fourier Integral Operators And Partial Differential Equations written by J. Chazarain and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.




The Analysis Of Linear Partial Differential Operators


The Analysis Of Linear Partial Differential Operators
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Author : Lars Hörmander
language : en
Publisher:
Release Date : 1983

The Analysis Of Linear Partial Differential Operators written by Lars Hörmander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Differential equations, Partial categories.




Global And Local Regularity Of Fourier Integral Operators On Weighted And Unweighted Spaces


Global And Local Regularity Of Fourier Integral Operators On Weighted And Unweighted Spaces
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Author : David Dos Santos Ferreira
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-07

Global And Local Regularity Of Fourier Integral Operators On Weighted And Unweighted Spaces written by David Dos Santos Ferreira 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 2014-04-07 with Mathematics categories.


The authors investigate the global continuity on spaces with of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in with . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted spaces, with and (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.