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＜電子ブック＞
Differential Equations on Complex Manifolds / by Boris Sternin, Victor Shatalov
(Mathematics and Its Applications ; 276)

版	1st ed. 1994.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1994
本文言語	英語
大きさ	XII, 508 p : online resource
著者標目	*Sternin, Boris author Shatalov, Victor author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Functions of complex variables LCSH:Mathematical analysis FREE:Differential Equations FREE:Several Complex Variables and Analytic Spaces FREE:Integral Transforms and Operational Calculus
一般注記	1 Some Questions of Analysis and Geometry of Complex Manifolds -- 2 Symplectic and Contact Structures -- 3 Integral Transformations of Ramified Analytic Functions -- 4 Laplace-Radon Integral Operators -- 5 Cauchy Problem in Spaces of Ramified Functions -- 6 Continuation of Solutions to Elliptic Equations 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 HTTP:URL=https://doi.org/10.1007/978-94-017-1259-0

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