Publisher's Synopsis
Analysis concerning the representation of distributions in the sense of L.Schwartz as boundary values of analytic functions in one and several variables is presented in this book. The contents review the facts concerning distributions and several complex variables and give detailed proofs of the analysis. Except for one section concerning vector valued distributions, the book concerns the scalar valued distributions as originally introduced by L.Schwartz.;Of particular interest throughout the development of one-dimensional boundary analysis is the construction and application of the distributional Plemelj relations. Throughout the book examples of the topics which are discussed are given and the one-dimensional distributional boundary value results are applied to yield solutions to distributional generalizations of boundary value problems of Plemlj, Hilbert, Reimann-Hilbert and Dirichlet and to convolution equations.;The text is aimed at mathematical physicists and engineers as well as mathematicians.
