Based on a series of lectures given to post-graduate students, this largely self-contained book makes distribution theory attainable to not only mathematics students, but also to those studying physics and engineering. It defines distributions using convergence concepts. Topics covered include Schwartz distributions, distributional derivatives, distributions of compact support, certain boundary value problems, and topological vector space theory.
Test Functions and Distributions. Convergence of Distributions. Differentiation of Distributions. Convolution of Distributions. Tempered Distributions and Fourier Transforms. Sobolev Spaces. Weak Solutions. Distributions on Locally Convex Spaces. Distributions on Manifolds. Bibliography. Index.