Fourier Integral Operators

Author:   J.J. Duistermaat
Publisher:   Birkhauser Boston Inc
ISBN:  

9780817681074


Pages:   142
Publication Date:   11 November 2010
Format:   Paperback
Availability:   In Print   Availability explained
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Fourier Integral Operators


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Full Product Details

Author:   J.J. Duistermaat
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Dimensions:   Width: 15.50cm , Height: 0.80cm , Length: 23.50cm
Weight:   0.510kg
ISBN:  

9780817681074


ISBN 10:   0817681078
Pages:   142
Publication Date:   11 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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.

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 as perhaps the very best place to start in the study of this subject. --SIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to non-specialists. --Zentralblatt MATH The book is completed with applications to the Cauchy problem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader should have some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. --Acta Sci. Math.


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 as perhaps the very best place to start in the study of this subject. -SIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to nonspecialists. -Zentralblatt MATH The book is completed with applications to the Cauchy problem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader should have some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. -Acta Sci. Math.


Author Information

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.

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