Problems in Distributions and Partial Differential Equations, Volume 143

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.

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.