Generalized Analytic Functions

✍ Scribed by Vekua I N

• Publisher: Pergamon Press
• Year: 1962
• Tongue: English
• Leaves: 672
• Category: Library

✦ Synopsis

Generalized Analytic Functions is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells. Some classes of functions and operators are discussed, along with the reduction of a positive differential quadratic form to the canonical form. Boundary value problems and infinitesimal bendings of surfaces are also considered.

Comprised of six chapters, this volume begins with a detailed treatment of various problems of the general theory of generalized analytic functions as as well as boundary value problems. The reader is introduced to some classes of functions and functional spaces, with emphasis on functions of two independent variables. Subsequent chapters focus on the problem of reducing a positive differential quadratic form to the canonical form; basic properties of solutions of elliptic systems of partial differential equations of the first order, in a two-dimensional domain; and some boundary value problems for an elliptic system of equations of the first order and for an elliptic equation of the second order, in a two-dimensional domain. The final part of the book deals with problems of the theory of surfaces and the membrane theory of shells.

This book is intended for students of advanced courses of the mechanico-mathematical faculties, postgraduates, and research workers.

✦ Table of Contents

Content:
OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS, Pages ii-iii
Front Matter, Pages iv-v
Copyright, Page vi
ANNOTATION, Page vii
FOREWORD, Pages xxvii-xxix
INTRODUCTION TO FOUNDATIONS OF THE GENERAL THEORY OF GENERALIZED ANALYTIC FUNCTIONS AND BOUNDARY VALUE PROBLEMS, Pages 1-3
CHAPTER I - SOME CLASSES OF FUNCTIONS AND OPERATORS, Pages 5-75
CHAPTER II - REDUCTION OF A POSITIVE DIFFERENTIAL QUADRATIC FORM TO THE CANONICAL FORM. BELTRAMI'S EQUATION. GEOMETRIC APPLICATIONS, Pages 76-129
CHAPTER III - FOUNDATIONS OF THE GENERAL THEORY OF GENERALIZED ANALYTIC FUNCTIONS, Pages 130-220
CHAPTER IV - BOUNDARY VALUE PROBLEMS, Pages 221-387
INTRODUCTION TO SOME APPLICATIONS TO PROBLEMS OF THE THEORY OF SURFACES AND THE MEMBRANE THEORY OF SHELLS, Page 389
CHAPTER V - FOUNDATIONS OF THE GENERAL THEORY OF INFINITESIMAL BENDINGS OF SURFACES, Pages 391-562
CHAPTER VI - PROBLEMS OF THE MEMBRANE THEORY OF SHELLS, Pages 563-645
REFERENCES, Pages 647-657
SUBJECT INDEX, Pages 659-668