Schwarz-pick type inequalities
By: Farit G. Avkhadiev, Karl-Joachim Wirths
Contributors: Wirths, Karl-Joachim
Series: Frontiers in mathematics
Publisher: Birkhäuser
Published: 2009
Place of publication: Basel; Boston
Language: eng
Number of pages: 156
ISBN-13: 9783764399993; 9783034600002
Subjects: Holomorphic functions; Funktionentheorie; Ungleichung; Geometric function theory
Description: This book discusses in detail the extension of the Schwarz-Pick inequality to higher order derivatives of analytic functions with given images. It is the first systematic account of the main results in this area. Recent results in geometric function theory presented here include the attractive steps on coefficient problems from Bieberbach to de Branges, applications of some hyperbolic characteristics of domains via Beardon-Pommerenke's theorem, a new interpretation of coefficient estimates as certain properties of the Poincaré metric, and a successful combination of the classical ideas of Littlewood, Löwner and Teichmüller with modern approaches. The material is complemented with historical remarks on the Schwarz Lemma and a chapter introducing some challenging open problems. The book will be of interest for researchers and postgraduate students in function theory and hyperbolic geometry.
Notes: Includes bibliographical references (p. [143]-153) and index.