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Fourier Integral Operators (Modern Birkhauser Classics)

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Fourier Integral Operators (Modern Birkhauser Classics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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 have caustics.

About the Author

Hans Duistermaat was a geometric analyst, who unexpectedly passed away in March 2010. His research encompassed many different areas in mathematics: ordinary differential equations, classical mechanics, discrete integrable systems, Fourier integral operators and their application to partial differential equations and spectral problems, singularities of mappings, harmonic analysis on semisimple Lie groups, symplectic differential geometry, and algebraic geometry. He was co-author of eleven books. Duistermaat was affiliated to the Mathematical Institute of Utrecht University since 1974 as a Professor of Pure and Applied Mathematics. During the last five years he was honored with a special professorship at Utrecht University endowed by the Royal Netherlands Academy of Arts and Sciences. He was also a member of the Academy since 1982. He had 23 PhD students.

Table of 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.

Product Details

ISBN:
9780817681074
Author:
Duistermaat, J. J.
Publisher:
Springer
Subject:
Mathematical Analysis
Subject:
Fourier transformation
Subject:
Lagragian manifolds
Subject:
global theory
Subject:
Integral operators.
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
symplectic differential geometry
Subject:
Wave propagation
Subject:
Fourier analysis
Subject:
Integral equations
Subject:
Operator theory
Subject:
Partial Differential Equations <p>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 a
Subject:
Mathematics-Analysis General
Copyright:
Edition Description:
2011
Series:
Modern Birkhäuser Classics
Publication Date:
20101111
Binding:
TRADE PAPER
Language:
English
Pages:
153
Dimensions:
235 x 155 mm 510 gr

Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Functional Analysis

Fourier Integral Operators (Modern Birkhauser Classics) New Trade Paper
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Product details 153 pages Springer - English 9780817681074 Reviews:
"Synopsis" by , 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 have caustics.
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