# The Analysis of Linear Partial Differential Operators II

## Differential Operators with Constant Coefficients

Part of the Classics in Mathematics book series (CLASSICS)

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Part of the Classics in Mathematics book series (CLASSICS)

This volume is an expanded version of Chapters III, IV, V and VII of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the monographs by Ehrenpreis and by Palamodov on this subject. The reader is assumed to be familiar with distribution theory as presented in Volume I. Most topics discussed here have in fact been encountered in Volume I in special cases, which should provide the necessary motivation and background for a more systematic and precise exposition. The main technical tool in this volume is the Fourier- Laplace transformation. More powerful methods for the study of operators with variable coefficients will be developed in Volume III. However, constant coefficient theory has given the guidance for all that work. Although the field is no longer very active - perhaps because of its advanced state of development - and although it is possible to pass directly from Volume I to Volume III, the material presented here should not be neglected by the serious student who wants to gain a balanced perspective of the theory of linear partial differential equations.

Complex analysis Distribution Theory Linear Partial Differential Operators analytic function convolution distribution fourier analysis scattering theory

- DOI https://doi.org/10.1007/b138375
- Copyright Information Springer-Verlag Berlin Heidelberg 2005
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-540-22516-4
- Online ISBN 978-3-540-26964-9
- Series Print ISSN 1431-0821
- Buy this book on publisher's site