Introduction to the Theory of Distributions / Edition 2

by F. G. Friedlander, M. Joshi

Overview

The theory of distributions is an extension of classical analysis, an area of particular importance in the field of linear partial differential equations. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without a knowledge of this. The material in this book, based on graduate lectures given over a number of years requires few prerequisites but the treatment is rigorous throughout. From the outset, the theory is developed in several variables. It is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces. In this second edition, the notion of the wavefront set of a distribution is introduced. It allows many operations on distributions to be extended to larger classes and gives much more precise understanding of the nature of the singularities of a distribution. This is done in an elementary fashion without using any involved theories. This account will be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics.

Product Details

ISBN-13:	9780521649711
Publisher:	Cambridge University Press
Publication date:	01/21/1999
Edition description:	Revised Edition
Pages:	188
Product dimensions:	5.98(w) x 9.02(h) x 0.43(d)

Table of Contents

1. Test functions and distributions; 2. Differentiation and multiplication; 3. Distributions and compact support; 4. Tensor products; 5. Convolution; 6. Distribution kernels; 7. Co-ordinate transforms and pullbacks; 8. Fourier transforms; 9. Plancherel's theorem; 10. The Fourier-Laplace transform; Appendix. Topological vector spaces; 11. The calculus of wavefront sets.

Editorial Reviews

"...a very clear, accurate and stimulating version of an important topic, with the emphasis in the right place and with the minimum of fuss." Bulletin of the London Mathematical Society

From the Publisher