相關主題
商品描述
Few other books purport to be a second course in complex analysis. This book differs in that it covers more modern topics and is more geometric in focus. Most texts on complex variable theory contain the same material. However, complex analysis is a vast and diverse subject with a long history and many aspects. A second course will benefit students and introduce these new topics that they might not otherwise experience.
Lars Ahlfors alone invented many new parts of the subject; Lipman Bers made decisive contributions, and there are many others. It is easy to justify a "second course" in complex analysis. That is what this book purports to be.
Some of the topics presented here are:
- harmonic measure
- extremal length
- Riemann surfaces
- uniformization
- automorphism groups
- the Schwarz lemma and its generalizations
- analytic capacity
- the Bergman theory
- invariant metrics
- Picard's theorem
- the boundary Schwarz lemma
The goal is to expose the reader to unfamiliar parts of the subject of complex variables and perhaps to pique interest in further reading. As with the authors' other books, not only theorems and proofs are included, but also many examples and some exercises. Numerous graphics illustrate the key ideas.
商品描述(中文翻譯)
少數幾本書聲稱是複變分析的第二門課程。本書的不同之處在於它涵蓋了更多現代主題，並且更注重幾何學。大多數有關複變數理論的教材包含相同的內容。然而，複變分析是一個廣泛且多樣的主題，擁有悠久的歷史和許多方面。第二門課程將使學生受益，並介紹這些他們可能不會接觸到的新主題。
拉斯·阿爾福斯（Lars Ahlfors）獨自發明了許多該領域的新部分；利普曼·伯斯（Lipman Bers）做出了決定性的貢獻，還有許多其他人。為複變分析提供一個「第二門課程」是很容易辯護的。這正是本書所聲稱的。
這裡呈現的一些主題包括：
- 輻射測度 (harmonic measure)
- 極長度 (extremal length)
- 黎曼面 (Riemann surfaces)
- 統一化 (uniformization)
- 自同構群 (automorphism groups)
- 施瓦茨引理及其推廣 (the Schwarz lemma and its generalizations)
- 解析容量 (analytic capacity)
- 貝爾曼理論 (the Bergman theory)
- 不變度量 (invariant metrics)
- 皮卡定理 (Picard's theorem)
- 邊界施瓦茨引理 (the boundary Schwarz lemma)
目標是讓讀者接觸到複變數主題中不熟悉的部分，並可能激發他們進一步閱讀的興趣。與作者的其他書籍一樣，不僅包含定理和證明，還有許多例子和一些練習題。大量圖形說明了關鍵概念。
作者簡介
Peter V. Dovbush, Dr. habil., is an Associate Professor at Moldova State University, in the Institute of Mathematics and Computer Science. He received his Ph.D. in Lomonosov Moscow State University in 1983 and Doctor of Sciences in 2003. He has published over 50 scholarly articles.
Steven G. Krantz is a Professor of Mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Penn State University. He received his Ph.D. from Princeton University in 1974. Krantz has directed 20 Ph.D. students and 8 Masters students. He has published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize and the Beckenbach Book Award and the Kemper Prize. He is a Fellow of the American Mathematical Society.
作者簡介(中文翻譯)
彼得·V·多夫布什（Peter V. Dovbush），博士，為摩爾多瓦國立大學數學與計算機科學研究所的副教授。他於1983年在莫斯科國立大學獲得博士學位，並於2003年獲得科學博士學位。他已發表超過50篇學術文章。
史蒂芬·G·克蘭茨（Steven G. Krantz）是聖路易華盛頓大學的數學教授。他曾在加州大學洛杉磯分校、普林斯頓大學和賓州州立大學任教。他於1974年在普林斯頓大學獲得博士學位。克蘭茨指導過20位博士生和8位碩士生。他已出版超過130本書籍和300篇學術文章。他是喬文內獎（Chauvenet Prize）、貝肯巴赫書獎（Beckenbach Book Award）和肯珀獎（Kemper Prize）的得主，也是美國數學學會的會士。
