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
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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

Function Theory of One Complex Variable: Third Edition

Base Product Code Keyword List: gsm/40; GSM/40; gsm; GSM; gsm/40.r; GSM/40.R; gsm-40.r; GSM-40.R; gsm-40; GSM-40; gsm-40-r; GSM-40-R

Print Product Code: GSM/40.R

Title (HTML): Function Theory of One Complex Variable: Third Edition

Author(s) (Product display): Robert E. Greene; Steven G. Krantz

Affiliation(s) (HTML): University of California, Los Angeles, Los Angeles, CA; Washington University, St. Louis, MO

Abstract:

Book Series Name: Graduate Studies in Mathematics

Volume: 40

Publication Month and Year: 2006-03-29

Page Count: 504

Cover Type: Hardcover

Print ISBN-13: 978-0-8218-3962-1

Print ISSN: 1065-7339

Primary MSC: 30

Textbook?: true

Applied Math?: false

MAA Book?: false

Electronic Media?: false

Apparel or Gift: false

SXG Subject: AN

Supplemental Materials (URL at AMS): https://www.ams.org/bookpages/gsm-40-r

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Print Price 2: 68.80

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Exam/Desk Copy: https://www.ams.org/exam-desk-review-request?&pisbn=978-0-8218-3962-1&ppc=GSM/40.R&title=Function%20Theory%20of%20One%20Complex%20Variable%3A%20Third%20Edition&author=Robert%20E.%20Greene%3B%20Steven%20G.%20Krantz&type=DE

Review Copy: https://www.ams.org/exam-desk-review-request?&pisbn=978-0-8218-3962-1&ppc=GSM/40.R&title=Function%20Theory%20of%20One%20Complex%20Variable%3A%20Third%20Edition&author=Robert%20E.%20Greene%3B%20Steven%20G.%20Krantz&type=R

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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Function Theory of One Complex Variable: Third Edition

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