Differential Equations on Complex Manifolds

1994
ISBN: 978-0-7923-2710-3
Verlag: Springer Netherlands

Buch, Englisch, 508 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 2000 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Shatalov, Victor

Sternin, Boris

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.