The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis

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Springer, Mar 30, 2015 - Mathematics - 440 pages
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 for numerous 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.
 

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Contents

Introduction
1
Definition and Basic Properties of Distributions
33
Differentiation and Multiplication by Functions
54
Convolution
87
Distributions in Product Spaces
126
Composition with Smooth Maps
133
The Fourier Transformation
158
Spectral Analysis of Singularities
251
Hyperfunctions
325
Exercises
371
Answers and Hints to All the Exercises
394
Bibliography
419
Index
437
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