Multivalent Functions
Seiten
2008
|
2nd Revised edition
Cambridge University Press (Verlag)
978-0-521-05767-7 (ISBN)
Cambridge University Press (Verlag)
978-0-521-05767-7 (ISBN)
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.
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.
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.
| Erscheint lt. Verlag | 28.1.2008 |
|---|---|
| Reihe/Serie | Cambridge Tracts in Mathematics |
| Zusatzinfo | Worked examples or Exercises; 5 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 454 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-521-05767-1 / 0521057671 |
| ISBN-13 | 978-0-521-05767-7 / 9780521057677 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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