Multivalent Functions

Essential reading for all interested in complex functions.

W. K. Hayman (Author)

9780521460262, Cambridge University Press

Hardback, published 24 November 1994

276 pages, 5 b/w illus. 70 exercises
22.9 x 15.2 x 1.9 cm, 0.533 kg

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.

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 Löwner theory
8. De Branges' Theorem
Bibliography
Index.

Subject Areas: Calculus & mathematical analysis [PBK]