Multivalent functions
著者
書誌事項
Multivalent functions
（Cambridge tracts in mathematics, 110）
Cambridge University Press, 2008
2nd ed
- : pbk
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注記
Includes bibliography (p. 255-260) and index
"First published 1958. Second edition 1994. This digitally printed version 2008"--T.p. verso
内容説明・目次
内容説明
The class of multivalent functions is an important one in complex analysis. They occur for example in the proof of De Branges' theorem which, in 1985, settled the long-standing Bieberbach conjecture. The second edition of Professor Hayman's celebrated book contains a full and self-contained proof of this result, with a chapter devoted to it. Another chapter deals with coefficient differences. It has been updated in several other ways, with theorems of Baernstein and Pommerenke on univalent functions of restricted growth, and an account of the theory of mean p-valent functions. In addition, many of the original proofs have been simplified. Each chapter contains examples and exercises of varying degrees of difficulty designed both to test understanding and illustrate the material. Consequently it will be useful for graduate students, and essential for specialists in complex function theory.
目次
- Preface
- 1. Elementary bounds for univalent functions
- 2. The growth of finitely mean valent functions
- 3. Means and coefficients
- 4. Symmetrization
- 5. Circumferentially mean p-valent functions
- 6. Differences of successive coefficients
- 7. The Loewner theory
- 8. De Branges' Theorem
- Bibliography
- Index.
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