
Fourier Integral Operators
J.J. Duistermaat(Author)
Birkhauser Boston Inc (Publisher)
1st Edition
Published on 29. November 1995
Book
Hardback
XII, 142 pages
978-0-8176-3821-4 (ISBN)
Description
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. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally, this book is designed for a one-semester introductory course on Fourier integral operators aimed at a broad audience.
More details
Series
Language
English
Place of publication
Secaucus
United States
Target group
Professional and scholarly
Graduate
Illustrations
9 s/w Abbildungen
3 b&w illustrations
Dimensions
Height: 235 mm
Width: 155 mm
Weight
440 gr
ISBN-13
978-0-8176-3821-4 (9780817638214)
Schweitzer Classification
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J.J. Duistermaat
Fourier Integral Operators
Book
11/2010
Birkhauser Boston Inc
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J.J. Duistermaat
Fourier Integral Operators
E-Book
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1st Edition
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Previous edition
Johannes J. Duistermaat
Fourier Integral Operators
Book
10/1995
Birkhäuser Verlag GmbH
€44.57
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Content
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.