Fourier Integral Operators

  • J.J. Duistermaat

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xi
  2. J. J. Duistermaat
    Pages 1-7
  3. J. J. Duistermaat
    Pages 8-22
  4. J. J. Duistermaat
    Pages 23-44
  5. J. J. Duistermaat
    Pages 45-90
  6. J. J. Duistermaat
    Pages 91-112
  7. J. J. Duistermaat
    Pages 113-137
  8. Back Matter
    Pages 138-142

About this book

Introduction

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 suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, resp. 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.

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.

Keywords

Distribution Fourier transform Fourier transformation Lagragian manifolds Operator Transformation calculus geometry global theory hyperbolic equation integral operators mechanics partial differential equation partial differential equations symplectic differential geometry

Authors and affiliations

  • J.J. Duistermaat
    • 1
  1. 1.Department of MathematicsUtrecht UniversityUtrechtNetherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8108-1
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8107-4
  • Online ISBN 978-0-8176-8108-1
  • About this book