| Differential Equations on Complex Manifolds Contributor(s): Sternin, Boris (Author), Shatalov, Victor (Author) |
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ISBN: 9048143683 ISBN-13: 9789048143689 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Mathematical Analysis |
| Dewey: 515.353 |
| Series: Mathematics and Its Applications |
| Physical Information: 1.05" H x 6.14" W x 9.21" (1.60 lbs) 508 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
