Overview
- Authors:
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Boris Sternin
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Moscow State University, Moscow, Russia
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Victor Shatalov
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Moscow Institute of Electronics and Mathematics, Moscow, Russia
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Table of contents (7 chapters)
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- Boris Sternin, Victor Shatalov
Pages 1-40
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- Boris Sternin, Victor Shatalov
Pages 41-136
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- Boris Sternin, Victor Shatalov
Pages 137-193
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- Boris Sternin, Victor Shatalov
Pages 195-249
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- Boris Sternin, Victor Shatalov
Pages 251-287
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- Boris Sternin, Victor Shatalov
Pages 289-404
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- Boris Sternin, Victor Shatalov
Pages 405-474
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Back Matter
Pages 475-508
About this book
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.
Authors and Affiliations
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Moscow State University, Moscow, Russia
Boris Sternin
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Moscow Institute of Electronics and Mathematics, Moscow, Russia
Victor Shatalov