Differential Equations on Complex Manifolds

ISBN-13: 9789048143689 / Angielski / Miękka / 2010 / 508 str.

Boris Sternin; Victor Shatalov

Opis

This volume contains a unique, systematic presentation of the general theory of differential equations on complex manifolds. The six chapters deal with questions concerning qualitative (asymptotic) theory of partial differential equations as well as questions about the existence of solutions in spaces of ramifying functions. Furthermore, much attention is given to applications. In particular, important problems connected with the continuation of (real) solutions to differential equations and with mathematical theory of diffraction are solved here. The book is self-contained, and includes up-to-date results. All necessary terminology is explained. For graduate students and researchers interested in differential equations in partial derivatives, complex analysis, symplectic and contact geometry, integral transformations and operational calculus, and mathematical physics.

Spis treści

Preface. Introduction. 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. Bibliography. Index.