Harmonic Measure

ISBN-13: 9780521470186 / Angielski / Twarda / 2005 / 588 str.

John B. Garnett; Donald E. Marshall

Opis

This book provides an enlightening survey of remarkable new results that have only recently been discovered in the past two decades about harmonic measure in the complex plane. Many of these results, due to Bishop, Carleson, Jones, Makarov, Wolff and others, appear here in paperback for the first time. The book is accessible to students who have completed standard graduate courses in real and complex analysis. The first four chapters provide the needed background material on univalent functions, potential theory, and extremal length, and each chapter has many exercises to further inform and teach the readers.

Recenzje

'… can be warmly recommended to students and researchers with a deep interest in analysis. It is an excellent preparation for serious work in complex analysis or potential theory.' EMS Newsletter

Spis treści

1. Jordan domains; 2. Finitely connected domains; 3. Potential theory; 4. Extremal distance; 5. Applications and reverse inequalities; 6. Simply connected domains, part one; 7. Bloch functions and quasicircles; 8. Simply connected domains, part two; 9. Infinitely connected domains; 10. Rectifiability and quadratic expressions; Appendices.