Several Complex Variables V : Complex Analysis in Partial Differential Equations and Mathematical Physics

Khenkin, G. M. (EDT); Berenstein, C. A. (CON); Morozov, A.yu. (CON); Novikov, R. G. (CON)

ISBN 10: 3642634338 / ISBN 13: 9783642634338

Published by Springer, 2012

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Bibliographic Details

• Title: Several Complex Variables V : Complex Analysis in Partial Differential Equations and Mathematical Physics
• Publisher: Springer
• Publication Date: 2012
• Language: English
• ISBN 10: 3642634338
• ISBN 13: 9783642634338
• Binding: Soft cover
• Condition: As New

About this title

Synopsis

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.

Language Notes

Text: English (translation)
Original Language: Russian