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  • © 2009

The Analysis of Linear Partial Differential Operators IV

Fourier Integral Operators

Authors:

  • Honours awarded to Lars Hörmander

  • Fields Medal 1962, Speaker at International Congress 1970, Wolf Prize 1988, AMS Steele Prize 2006

  • Includes supplementary material: sn.pub/extras

Part of the book series: Classics in Mathematics (CLASSICS)

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  • ISBN: 978-3-642-00136-9
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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
  2. Introduction

    • Lars Hörmander
    Pages 1-2
  3. Subelliptic Operators

    • Lars Hörmander
    Pages 165-219
  4. Uniqueness for the Cauchy Problem

    • Lars Hörmander
    Pages 220-248
  5. Spectral Asymptotics

    • Lars Hörmander
    Pages 249-275
  6. Long Range Scattering Theory

    • Lars Hörmander
    Pages 276-331
  7. Back Matter

    Pages 332-352

About this book

From the reviews:

"Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators."
L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987

"This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation."
J. Brüning in Zentralblatt MATH, 1987

Keywords

  • 35P2
  • Boundary value problems on manifolds
  • Distribution
  • Propagation of singularities
  • Spectral problems
  • analysis
  • calculus
  • initial value problems
  • operators
  • partial differential equation
  • partial differential equations
  • pseudodifferential operators
  • scattering theory
  • spectral geometry

Reviews

From the reviews:

"Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987.

"This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987.

“The fourth volume of the impressive monograph "The Analysis of Partial Differential Operators'' by Lars Hörmander continues the detailed and unified approach of pseudo-differential and Fourier integral operators. The present book is a paperback edition of the fourth volume of this monograph. … The book has been one of the most elegant, inspiring and influential texts in Mathematics, and contains results used in many important developments in Partial Differential Equations and Mathematical Physics.” (Viorel Iftimie, Zentralblatt MATH, Vol. 1178, 2010)

Authors and Affiliations

  • Department of Mathematics, University of Lund, Lund, Sweden

    Lars Hörmander

About the author

Biography Lars Hörmander

Born on January 24, 1931, on the southern coast of Sweden, Lars Hörmander did his secondary schooling as well as his undergraduate and doctoral studies in Lund. His principle teacher and adviser at the University of Lund was Marcel Riesz until he returned, then Lars Gårding. In 1956 he worked in the USA, at the universities of Chicago, Kansas, Minnesota and New York, before returning to a chair at the University of Stockholm. He remained a frequent visitor to the US, particularly to Stanford and was Professor at the IAS, Princeton from 1964 to 1968. In 1968 he accepted a chair at the University of Lund, Sweden, where, today, he is Emeritus Professor.

Hörmander’s lifetime work has been devoted to the study of partial differential equations and its applications in complex analysis. In 1962 he was awarded the Fields Medal for his contributions to the general theory of linear partial differential operators. His book Linear Partial Differential Operators published 1963 by Springer in the Grundlehren series was the first major account of this theory. His four volume text The Analysis of Linear Partial Differential Operators published in the same series 20 years later illustrates the vast expansion of the subject in that period.

Bibliographic Information

  • Book Title: The Analysis of Linear Partial Differential Operators IV

  • Book Subtitle: Fourier Integral Operators

  • Authors: Lars Hörmander

  • Series Title: Classics in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-00136-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2009

  • Softcover ISBN: 978-3-642-00117-8

  • eBook ISBN: 978-3-642-00136-9

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 1

  • Number of Pages: VII, 352

  • Additional Information: Originally published as Volume 275 in the series: Grundlehren der mathematischen Wissenschaften

  • Topics: Real Functions, Analysis

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-00136-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 69.99
Price excludes VAT (USA)