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  1. Home
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  3. Multivalent Functions
  • Cited by 103
Publisher:
Cambridge University Press
Online publication date:
November 2009
Print publication year:
1994
Online ISBN:
9780511526268
DOI:
https://doi.org/10.1017/CBO9780511526268
Subjects:
Mathematics (general), Mathematics, Real and Complex Analysis
Series:
Cambridge Tracts in Mathematics (110)
Information

Book description

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.

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