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Differential Equations on Complex Manifolds : Mathematics and Its Applications - B.IU Sternin

Differential Equations on Complex Manifolds

Mathematics and Its Applications

Hardcover

Published: 28th February 1994
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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.

Preface
Introductionp. 1
Some Questions of Analysis and Geometry of Complex Manifoldsp. 41
Symplectic and Contact Structuresp. 137
Integral Transformations of Ramified Analytic Functionsp. 195
Laplace-Radon Integral Operatorsp. 251
Cauchy Problem in Spaces of Ramified Functionsp. 289
Continuation of Solutions to Elliptic Equationsp. 405
Bibliographyp. 475
Indexp. 501
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792327103
ISBN-10: 0792327101
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 508
Published: 28th February 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 3.18
Weight (kg): 2.0