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Modern Birkhäuser Classics

Fourier Integral Operators

Authors: Duistermaat, J.J.

  • Based on author’s original lecture notes
  • Covers a broad range of topics
  • Useful for both practitioners and students
  • Applications put theory in context
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  • ISBN 978-0-8176-8108-1
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  • ISBN 978-0-8176-8107-4
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About this Textbook

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.

About the authors

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.

Reviews

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 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.

“Duistermaat’s Fourier Integral Operators had its genesis in a course the author taught at Nijmegen in 1970. … For the properly prepared and properly disposed mathematical audience Fourier Integral Operators is a must. … it is a very important book on a subject that is both deep and broad.” (Michael Berg, The Mathematical Association of America, May, 2011)


Table of contents (6 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-0-8176-8108-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-0-8176-8107-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Fourier Integral Operators
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-8108-1
DOI
10.1007/978-0-8176-8108-1
Softcover ISBN
978-0-8176-8107-4
Series ISSN
2197-1803
Edition Number
1
Number of Pages
IX, 142
Topics