Differential Equations on Complex Manifolds: 276 (Mathematics and Its Applications, 276) - Hardcover

Sternin, Boris; Shatalov, Victor

Hardcover

ISBN 10: 0792327101 ISBN 13: 9780792327103

Publisher: Springer, 1994

Synopsis

The present monograph is devoted to the complex theory of differential equations. Not yet a handbook, neither a simple collection of articles, the book is a first attempt to present a more or less detailed exposition of a young but promising branch of mathematics, that is, the complex theory of partial differential equations. Let us try to describe the framework of this theory. First, simple examples show that solutions of differential equations are, as a rule, ramifying analytic functions. and, hence, are not regular near points of their ramification. Second, bearing in mind these important properties of solutions, we shall try to describe the method solving our problem. Surely, one has first to consider differential equations with constant coefficients. The apparatus solving such problems is well-known in the real the­ ory of differential equations: this is the Fourier transformation. Un­ fortunately, such a transformation had not yet been constructed for complex-analytic functions and the authors had to construct by them­ selves. This transformation is, of course, the key notion of the whole theory.

About this title

Synopsis

This volume contains a unique, systematic presentation of the general theory of differential equations on complex manifolds. The six chapters deal with questions concerning qualitative (asymptotic) theory of partial differential equations as well as questions about the existence of solutions in spaces of ramifying functions. Furthermore, much attention is given to applications. In particular, important problems connected with the continuation of (real) solutions to differential equations and with mathematical theory of diffraction are solved here. The book is self-contained, and includes up-to-date results. All necessary terminology is explained. This volume is intended for graduate students and researchers interested in differential equations in partial derivatives, complex analysis, symplectic and contact geometry, integral transformations and operational calculus, and mathematical physics.

Edition details

• Publisher: Springer
• Publication date: 1994
• Language: English
• ISBN 10: 0792327101
• ISBN 13: 9780792327103
• Binding: Hardcover
• Number of pages: 520