Encyclopaedia of Mathematical Sciences

Several Complex Variables V

Complex Analysis in Partial Differential Equations and Mathematical Physics

Editors: Khenkin, G.M. (Ed.)

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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.

Table of contents (3 chapters)

  • Complex Analysis and Convolution Equations

    Berenstein, C. A. (et al.)

    Pages 1-108

  • The Yang–Mills Fields, the Radon–Penrose Transform, and the Cauchy–Riemann Equations

    Khenkin, G. M. (et al.)

    Pages 109-193

  • Complex Geometry and String Theory

    Morozov, A. Yu. (et al.)

    Pages 195-280

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-58011-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-3-642-63433-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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
Series Volume
54
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-58011-6
DOI
10.1007/978-3-642-58011-6
Softcover ISBN
978-3-642-63433-8
Series ISSN
0938-0396
Edition Number
1
Number of Pages
VII, 287
Additional Information
Originally published by VINITI, Moscow 1989
Topics