The Analysis of Linear Partial Differential Operators I

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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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.

• analytic function
• differential calculus
• differential equation
• distribution
• fourier analysis
• Fourier transform
• harmonic analysis
• integral
• Laplace transform
• manifold
• partial differential equation
• Smooth function

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

  Lars Hörmander

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