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Function Theory of One Complex Variable: Third Edition
Robert E. Greene, University of California, Los Angeles, CA, and Steven G. Krantz, Washington University, St. Louis, MO
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Graduate Studies in Mathematics
2006; 504 pp; hardcover
Volume: 40
ISBN-10: 0-8218-3962-4
ISBN-13: 978-0-8218-3962-1
List Price: US$81
Member Price: US$64.80
Order Code: GSM/40.R
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See also:

An Introduction to Complex Analysis and Geometry - John P D'Angelo

Complex Made Simple - David C Ullrich

Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point.

The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat \(H^p\) spaces and Painlevé's theorem on smoothness to the boundary for conformal maps.

This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

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Readership

Graduate students interested in complex analysis.

Reviews

"I can say that I have read this book with great pleasure and I do recommend it for those who are interested in complex analysis."

-- Zentralblatt MATH

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