Function Theory of Several Complex Variables (AMS Chelsea Publishing)
| Author | : | |
| Rating | : | 4.18 (918 Votes) |
| Asin | : | 0821827243 |
| Format Type | : | paperback |
| Number of Pages | : | 564 Pages |
| Publish Date | : | 2016-10-29 |
| Language | : | English |
DESCRIPTION:
the student needs a book like Krantz's, which is written as a text with explainations and exercises." ---- Bulletin of the American Mathematical Society . "This book makes available a comprehensive, detailed and carefully organized treatment of the foundations for multidimensional complex analysis. provides all sorts of topics and exercises which stretch the imagination and show how useful the subject really is." ---- Zentralblatt MATH"One of the remarkable features of this book is that it contains a large number of exercises and problems
. Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published more than 150 research articles and over 50 books. He has worked as an editor of several book series, research journals, and for the Notices of the AMS
This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory. It is currently the only book on the subject with exercises and a large number of examples.. While due homage is paid to the more traditional algebraic theory (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment
Kevin M. Iga said readable and engaging, good introduction to subject. Krantz has a very readable style and this is one math book that is fun reading (assuming you have the background listed above). No definition causes you to wonder why it was defined, and no theorem causes you to wonder why it was proved.It's also one of the few books that defines sheaf cohomology in terms of actual geometric intuition and concrete examples. Even readers not interested in several complex variables should benefit from the way he treats tangential subjects in this book.. Not good but probably the best there is in the subject. I really wish there was a better book in the subject. I've had a course in measure theory and complex analysis of a single variable, and I am woefully underprepared for this book. You need to be very fresh with multivariable calculus and differential geometry to have any hope doing the exercises, and the appendices don't prepare you much at all to review those things or guide you towards looking for the tools you need. The author leaves a ton of remarks as exercises, to the point where reading alone would leave you with a greater than average learning gap. but this looks like the best of the bunch robert clarke This book is a gem! Krantz' breezy style is magnificent, but he never flinches from the details. Loaded with examples and intuitive remarks, he helps the reader dig through the details of complex concepts. (Take a look at his treatment of domains of holomorphy in C^1 contrasted with C^n.) I have tried to slog through Gunning and Rossi and have looked hard at Hormander, but this looks like the best of the bunch. Highly recommended, but come prepared.