# The Analysis of Linear Partial Differential Operators I

## Distribution Theory and Fourier Analysis

• Authors
• Lars Hörmander
Book

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 256)

1. Front Matter
Pages I-IX
2. Lars Hörmander
Pages 1-4
3. Lars Hörmander
Pages 5-32
4. Lars Hörmander
Pages 33-53
5. Lars Hörmander
Pages 54-86
6. Lars Hörmander
Pages 87-125
7. Lars Hörmander
Pages 126-132
8. Lars Hörmander
Pages 133-157
9. Lars Hörmander
Pages 158-250
10. Lars Hörmander
Pages 251-324
11. Lars Hörmander
Pages 325-370
12. Back Matter
Pages 371-394

### Introduction

In 1963 my book entitled "Linear partial differential operators" was published in the Grundlehren series. Some parts of it have aged well but others have been made obsolete for quite some time by techniques using pseudo-differential and Fourier integral operators. The rapid de­ velopment has made it difficult to bring the book up to date. Howev­ er, the new methods seem to have matured enough now to make an attempt worth while. The progress in the theory of linear partial differential equations during the past 30 years owes much to the theory of distributions created by Laurent Schwartz at the end of the 1940's. It summed up a great deal of the experience accumulated in the study of partial differ­ ential equations up to that time, and it has provided an ideal frame­ work for later developments. "Linear partial differential operators" be­ gan with a brief summary of distribution theory for this was still un­ familiar to many analysts 20 years ago. The presentation then pro­ ceeded directly to the most general results available on partial differ­ ential operators. Thus the reader was expected to have some prior fa­ miliarity with the classical theory although it was not appealed to ex­ plicitly. Today it may no longer be necessary to include basic distribu­ tion theory but it does not seem reasonable to assume a classical background in the theory of partial differential equations since mod­ ern treatments are rare.

### Keywords

Distribution Harmonische Analyse Operators development differential equation differential operator equation integral partial differential equation presentation techniques time

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-96750-4
• Copyright Information Springer-Verlag Berlin Heidelberg 1998
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-642-96752-8
• Online ISBN 978-3-642-96750-4
• Series Print ISSN 0072-7830
• Buy this book on publisher's site