© 1993

Several Complex Variables V

Complex Analysis in Partial Differential Equations and Mathematical Physics

  • G. M. Khenkin

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 54)

Table of contents

  1. Front Matter
    Pages i-vii
  2. C. A. Berenstein, D. C. Struppa
    Pages 1-108
  3. A. Yu. Morozov, A. M. Perelomov
    Pages 195-280
  4. Back Matter
    Pages 281-287

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.


Koordinatentransformation Radon-Penrose Radon-Penrose-Transformierte Stringtheorie complex analysis complex geometry differential geometry field theory general relativity geometry komplexe Geometrie quantum field theory relativity theory of relativity transforms

Editors and affiliations

  • G. M. Khenkin
    • 1
  1. 1.Université de Paris VI, Pierre et Marie Curie, Mathématiques Paris Cedex 05France

Bibliographic information

  • Book Title Several Complex Variables V
  • Book Subtitle Complex Analysis in Partial Differential Equations and Mathematical Physics
  • Editors G.M. Khenkin
  • Series Title Encyclopaedia of Mathematical Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-54451-7
  • Softcover ISBN 978-3-642-63433-8
  • eBook ISBN 978-3-642-58011-6
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages VII, 287
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by VINITI, Moscow 1989
  • Topics Analysis
    Differential Geometry
    Theoretical, Mathematical and Computational Physics
  • Buy this book on publisher's site