Description
Book SynopsisThe theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide a
Trade ReviewIt is a pure pleasure to read: the prose is crystal clear and anything but prolix. ... They are happy to get into relatively elementary material in some detail, and sophisticated stuff. And the i's are dotted and the t's are crossed. It's a wonderful book!" —
MAA ReviewsTable of Contents
- Holomorphic functions
- Local rings of holomorphic functions
- Varieties
- Analytic sheaves
- Analytic spaces
- Cohomology theory
- Stein spaces, geometric theory
- Stein spaces, sheaf theory
- Pseudoconvexity
- Partitions of unity
- The theorem of Schwartz on Frechet spaces
- References
- Bibliography
- Index
