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Mathematics - Analysis | Several Complex Variables V - Complex Analysis in Partial Differential Equations and Mathematical

Several Complex Variables V

Complex Analysis in Partial Differential Equations and Mathematical Physics

Khenkin, G.M. (Ed.)

Originally published by VINITI, Moscow 1989

Softcover reprint of the original 1st ed. 1993, VII, 287 p.

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  • About this book

In this part, we present a survey of mean-periodicity phenomena which arise in connection with classical questions in complex analysis, partial differential equations, and more generally, convolution equations. A common feature of the problem we shall consider is the fact that their solutions depend on tech­ niques and ideas from complex analysis. One finds in this way a remarkable and fruitful interplay between mean-periodicity and complex analysis. This is exactly what this part will try to explore. It is probably appropriate to stress the classical flavor of all of our treat­ ment. Even though we shall frequently refer to recent results and the latest theories (such as algebmic analysis, or the theory of Bernstein-Sato polyno­ mials), it is important to observe that the roots of probably all the problems we discuss here are classical in spirit, since that is the approach we use. For instance, most of Chap. 2 is devoted to far-reaching generalizations of a result dating back to Euler, and it is soon discovered that the key tool for such gen­ eralizations was first introduced by Jacobi! As the reader will soon discover, similar arguments can be made for each of the subsequent chapters. Before we give a complete description of our work on a chapter-by-chapter basis, let us make a remark about the list of references. It is quite hard (maybe even impossible) to provide a complete list of references on such a vast topic.

Content Level » Research

Keywords » Convolution equations - Faltungsgleichungen - Radon-Penrose - Radon-Penrose-Transformierte - Stringtheorie - Yang-Mills Felder - Yang-Mills fields - complex geometry - komplexe Geometrie - string theory - transforms

Related subjects » Analysis - Geometry & Topology - Theoretical, Mathematical & Computational Physics

Table of contents 

I. Complex Analysis and Convolution Equations.- II. The Yang-Mills Fields, the Radon-Penrose Transform and the Cauchy-Riemann Equations.- III. Complex Geometry and String Theory.- Author Index.

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