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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.

Inhaltsverzeichnis

Frontmatter

I. Complex Analysis and Convolution Equations

Abstract
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 techniques 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.
C. A. Berenstein, D. C. Struppa

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

Abstract
In this part, we consider a number of problems of complex analysis and mathematical physics connected with the theory of Yang-Mills gauge fields on the one hand and the theory of Cauchy-Riemann equations on the other.
G. M. Khenkin, R. G. Novikov

III. Complex Geometry and String Theory

Abstract
String theory is a rather new field of theoretical physics. It appeared only twenty years ago to describe phenomenology of strong interactions of elementary particles, and until recently, it has been developing rather slowly. This is because string theory has encountered a number of difficulties that were not easy to overcome; in particular, this theory contained the so-called anomalies that hindered construction of self-consistent string theory. Especially, anomalies led to the breakdown of symmetry properties of this theory after its quantization.
A. Yu. Morozov, A. M. Perelomov

Backmatter

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