Several Complex Variables V

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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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

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

  G. M. Khenkin

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