Boundary Value Problems

✍ Scribed by F.D. Gakhov

• Publisher: Pergamon Press
• Year: 1966
• Tongue: English
• Leaves: 572
• Category: Library

✦ Synopsis

Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions.
The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotskis formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed.
The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
FOREWORD TO THE FIRST EDITION, Pages xiii-xvi
FOREWORD TO THE SECOND EDITION, Page xvii
INTRODUCTION, Page xix
CHAPTER I - INTEGRALS OF THE CAUCHY TYPE, Pages 1-84
CHAPTER II - RIEMANN BOUNDARY VALUE PROBLEM, Pages 85-142
CHAPTER III - SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNEL, Pages 143-206
CHAPTER IV - HILBERT BOUNDARY VALUE PROBLEM AND SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL, Pages 207-289
CHAPTER V - VARIOUS GENERALIZED BOUNDARY VALUE PROBLEMS†, Pages 290-405
CHAPTER VI - BOUNDARY VALUE PROBLEMS AND SINGULAR INTEGRAL EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND OPEN CONTOURS, Pages 406-493
CHAPTER VII - INTEGRAL EQUATIONS SOLUBLE IN CLOSED FORM, Pages 494-550
REFERENCES, Pages 551-558
INDEX, Pages 559-561
OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS, Pages 562-564