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Fourier Integral Operators

Author: J J Duistermaat
Publisher: Boston : Birkhäuser Boston, 2011.
Series: Modern Birkhäuser classics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 applications to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J J Duistermaat
ISBN: 0817681086 9780817681081 9780817681074 0817681078
OCLC Number: 1058601815
Language Note: English.
Description: 1 online resource (IX, 142 pages).
Contents: Preface --
0. Introduction --
1. Preliminaries --
1.1 Distribution densities on manifolds --
1.2 The method of stationary phase --
1.3 The wave front set of a distribution --
2. Local Theory of Fourier Integrals --
2.1 Symbols --
2.2 Distributions defined by oscillatory integrals --
2.3 Oscillatory integrals with nondegenerate phase functions --
2.4 Fourier integral operators (local theory) --
2.5 Pseudodifferential operators in Rn --
3. Symplectic Differential Geometry --
3.1 Vector fields --
3.2 Differential forms --
3.3 The canonical 1- and 2-form T* (X) --
3.4 Symplectic vector spaces --
3.5 Symplectic differential geometry --
3.6 Lagrangian manifolds --
3.7 Conic Lagrangian manifolds --
3.8 Classical mechanics and variational calculus --
4. Global Theory of Fourier Integral Operators --
4.1 Invariant definition of the principal symbol --
4.2 Global theory of Fourier integral operators --
4.3 Products with vanishing principal symbol --
4.4 L2-continuity --
5. Applications --
5.1 The Cauchy problem for strictly hyperbolic differential operators with C-infinity coefficients --
5.2 Oscillatory asymptotic solutions. Caustics --
References.
Series Title: Modern Birkhäuser classics.
Other Titles: Modern Birkhäuser Classics
Responsibility: by J.J. Duistermaat.

Abstract:

This useful introduction to Fourier Integral Operators approaches the subject from symplectic geometry and includes application to hyperbolic equations and oscillatory asymptotic solutions which may  Read more...

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From the reviews:This book remains a superb introduction to the theory of Fourier integral operators. While there are further advances discussed in other sources, this book can still be recommended Read more...

 
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