Several Complex Variables V

Complex Analysis in Partial Differential Equations and Mathematical Physics

Buch | Softcover

VII, 287 Seiten

2012 | 1. Softcover reprint of the original 1st ed. 1993
Springer Berlin (Verlag)
978-3-642-63433-8 (ISBN)

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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.

I. Complex Analysis and Convolution Equations.- II. The Yang-Mills Fields, the Radon-Penrose Transform and the Cauchy-Riemann Equations.- III. Complex Geometry and String Theory.- Author Index.

Erscheint lt. Verlag	5.11.2012
Reihe/Serie	Encyclopaedia of Mathematical Sciences
Co-Autor	C.A. Berenstein, G.M. Khenkin, A.Yu. Morozov, R.G. Novikov, A.M. Perelomov, D.C. Struppa
Zusatzinfo	VII, 287 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	457 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Analysis • Complex Analysis • complex geometry • Convolution equations • Differential Geometry • Faltungsgleichungen • Field Theory • General relativity • Geometry • komplexe Geometrie • Koordinatentransformation • quantum field theory • Radon-Penrose • Radon-Penrose-Transformierte • Relativity • Stringtheorie • String Theory • Theory of relativity • Transforms • Yang-Mills Felder • Yang-Mills fields
ISBN-10	3-642-63433-8 / 3642634338
ISBN-13	978-3-642-63433-8 / 9783642634338
Zustand	Neuware