Differential Equations on Complex Manifolds

By: Boris Sternin, Victor Shatalov

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Hardcover | 28 February 1994

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524 Pages

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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.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis Differential Calculus & Equations

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Published: 6th December 2010

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Preface
Introduction	p. 1
Some Questions of Analysis and Geometry of Complex Manifolds	p. 41
Symplectic and Contact Structures	p. 137
Integral Transformations of Ramified Analytic Functions	p. 195
Laplace-Radon Integral Operators	p. 251
Cauchy Problem in Spaces of Ramified Functions	p. 289
Continuation of Solutions to Elliptic Equations	p. 405
Bibliography	p. 475
Index	p. 501
Table of Contents provided by Blackwell. All Rights Reserved.

Differential Equations on Complex Manifolds

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Hardcover

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