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The Analysis of Linear Partial Differential Operators I

Distribution Theory and Fourier Analysis

  • Book
  • © 2003

Overview

Authors:
  1. Lars Hörmander

    1. Department of Mathematics, University of Lund, Lund, Sweden

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    • Lars Hörmander
    Pages 1-4

  3. Test Functions

    • Lars Hörmander
    Pages 5-32

  4. Definition and Basic Properties of Distributions

    • Lars Hörmander
    Pages 33-53

  5. Differentiation and Multiplication by Functions

    • Lars Hörmander
    Pages 54-86

  6. Convolution

    • Lars Hörmander
    Pages 87-125

  7. Distributions in Product Spaces

    • Lars Hörmander
    Pages 126-132

  8. Composition with Smooth Maps

    • Lars Hörmander
    Pages 133-157

  9. The Fourier Transformation

    • Lars Hörmander
    Pages 158-250

  10. Spectral Analysis of Singularities

    • Lars Hörmander
    Pages 251-324

  11. Hyperfunctions

    • Lars Hörmander
    Pages 325-370

  12. Back Matter

    Pages 371-440
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Keywords

About this book

The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen­ tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen­ eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and fornumerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.

Authors and Affiliations

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

    Lars Hörmander

Bibliographic Information

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

  • Book Subtitle: Distribution Theory and Fourier Analysis

  • Authors: Lars Hörmander

  • Series Title: Classics in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-61497-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2003

  • Softcover ISBN: 978-3-540-00662-6Published: 07 July 2003

  • eBook ISBN: 978-3-642-61497-2Published: 30 March 2015

  • Series ISSN: 1431-0821

  • Series E-ISSN: 2512-5257

  • Edition Number: 2

  • Number of Pages: XI, 440

  • Topics: Analysis

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