Raghavan Narasimhan - Böcker

Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramified domains over C . Topics discussed are Hartogs' theory, domains in holomorphy, and automorphism of bounded domains.

This volume presents complex analysis in one variable in the context of modern mathematics, with connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Covering spaces are used in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions on a domain in C is studied. The book illustrates mathematical ideas and tools. Cohomological methods are introduced, in connection with the existence of primatives and in the study of meromorphic funtion as on a compact Riemann surface. This second edition has exercises, problems and examples for students, so they can consolidate their command of complex analysis and its relations to other branches of mathematics.

The original edition of this book has been out of print for some years. Since the book was first published, several people have remarked on the absence of exercises and expressed the opinion that the book would have been more useful had exercises been included.