The second edition of this celebrated book contains a full and self-contained proof of De Branges' theorem. Every chapter has been updated and many of the original proofs have been simplified. It will be essential for all interested in complex function theory.
Inhaltsverzeichnis
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.
Klappentext
Multivalent and in particular univalent functions play an important role in complex analysis. Great interest was aroused when de Branges in 1985 settled the long-standing Bieberbach conjecture for the coefficients of univalent functions. The second edition of Professor Hayman's celebrated book is the first to include a full and self-contained proof of this result, with a new chapter devoted to it. Another new chapter deals with coefficient differences of mean p-valent functions. The book has been updated in several other ways, with recent theorems of Baernstein and Pommerenke on univalent functions of restricted growth and Eke's regularity theorems for the behaviour of the modulus and coefficients of mean p-valent functions. Some of the original proofs have been simplified. Each chapter contains examples and exercises of varying degrees of difficulty designed both to test understanding and to illustrate the material. Consequently the book will be useful for graduate students and essential for specialists in complex function theory.
