**Graduate Studies in Mathematics**

Volume: 40;
2006;
504 pp;
Hardcover

MSC: Primary 30;
**Print ISBN: 978-0-8218-3962-1
Product Code: GSM/40.R**

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

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#### Supplemental Materials

# Function Theory of One Complex Variable: Third Edition

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*Robert E. Greene; Steven G. Krantz*

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.

#### Readership

Graduate students interested in complex analysis.

#### Reviews & Endorsements

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