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Several Complex Variables V

Complex Analysis in Partial Differential Equations and Mathematical Physics

  • Book
  • © 1993

Overview

Editors:
  1. G. M. Khenkin

    1. Université de Paris VI, Pierre et Marie Curie, Mathématiques , Paris Cedex 05, France

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

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-vii
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  2. Complex Analysis and Convolution Equations

    • C. A. Berenstein, D. C. Struppa
    Pages 1-108

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

    • G. M. Khenkin, R. G. Novikov
    Pages 109-193

  4. Complex Geometry and String Theory

    • A. Yu. Morozov, A. M. Perelomov
    Pages 195-280

  5. Back Matter

    Pages 281-287
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Keywords

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.

Editors and Affiliations

  • Université de Paris VI, Pierre et Marie Curie, Mathématiques , Paris Cedex 05, France

    G. M. Khenkin

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: https://doi.org/10.1007/978-3-642-58011-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Hardcover ISBN: 978-3-540-54451-7Published: 06 December 1993

  • Softcover ISBN: 978-3-642-63433-8Published: 05 November 2012

  • eBook ISBN: 978-3-642-58011-6Published: 06 December 2012

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: VII, 287

  • Additional Information: Originally published by VINITI, Moscow 1989

  • Topics: Analysis, Differential Geometry, Theoretical, Mathematical and Computational Physics

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