Boundary Value Problems for Analytic Functions (Series in Pure Mathematics)

This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincare-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which were not published in English and, hence, were previously unknown to most readers in the world. This book consists of seven chapters together with an appendix: chapter 1 describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals, chapters II and III study respectively fundamental boundary value problems and their applications to singular integral equations for closed contours, chapters IV and V discuss the same problems for curves with nodes (including open arcs), chapter VI deals with similar problems for systems of functions, chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of those exercises.