Problems in distributions and partial differential equations
Author(s)
Bibliographic Information
Problems in distributions and partial differential equations
（North-Holland mathematics studies, 143）
North-Holland , Sole distributers for the U.S.A. and Canada by Elsevier Science Pub., 1988
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Problèmes des distributions
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:515.3/Z842070085003
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Note
Originally published as Problèmes des distributions: Paris : Hermann, 1988
Bibliography: p. 241
Includes index
Description and Table of Contents
Description
The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists.The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.
Table of Contents
1. Preliminaries. 2. Distributions. 3. Differentiation in the Space of Distributions. 4. Convergence in the Spaces of Distributions. 5. Convolution of Distributions. 6. Fourier and Laplace Transforms of Distributions. 7. Applications. Bibliography. Index. Index of Notations.
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