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Function Theory of One Complex Variable

Robert Everist GreeneSteven George Krantz

出版	American Mathematical Soc., 2006
主題	Mathematics / CalculusMathematics / Complex Analysis
ISBN	08218396249780821839621
URL	http://books.google.com.hk/books?id=u5vhseYCcqkC&hl=&source=gbs_api
EBook	SAMPLE

註釋

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 andexercises 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 $Hp$ spaces and Painleve'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.