Applications of generalized condensers to analytic function theory

被引：7

作者：

Dubinin V.N. ^{[1
]}

Eyrikh N.V. ^{[1
]}

机构：

[1] Institute of Applied Mathematics, Far-Eastern Branch, Russian Academy of Sciences, Vladivostock

来源：

Journal of Mathematical Sciences | 2006年 / 133卷 / 6期

基金：

俄罗斯基础研究基金会;

关键词：

Analytic Function; Univalent Function; Function Theory; Simple Property; Schwarzian Derivative;

D O I：

10.1007/s10958-006-0076-z

中图分类号：

学科分类号：

摘要：

New applications of generalized condensers with two or more plates are considered. Based on one and the same approach and simplest properties of such condensers, boundary distortion theorems for analytic univalent functions bounded in a disk are established, as well as bounds for certain combinations of coefficients in expansions of such functions, inequalities for polynomials, and theorems on extremal decompositions of the complex sphere. Part of the results obtained contains new information on the Schwarzian derivative of a regular univalent function. Bibliography: 21 titles. © 2006 Springer Science+Business Media, Inc.

引用

页码：1634 / 1647

页数：13

共 21 条

[1]

Dubinin V.N., Symmetrization in the geometric theory of functions of a complex variable, Usp. Mat. Nauk, 49, 1, pp. 3-76, (1994)

[2]

Dubinin V.N., Capacities of Condensers in Geometric Function Theory, (2003)

[3]

Kuz'Mina G.V., Methods of geometric function theory. II, Algebra Analiz, 9, 5, pp. 1-50, (1997)

[4]

Solynin A.Y., Modules and extremal-metric problems, Algebra Analiz, 11, 1, pp. 3-86, (1999)

[5]

Dubinin V.N., Eyrikh N.V., The generalized reduced module, Dal'nevost. Mat. Zh., 3, 2, pp. 150-164, (2002)

[6]

Dubinin V.N., Generalized condensers and the asymptotics of their capacities under degeneration of some plates, Zap. Nauchn. Semim. POMI, 302, pp. 38-51, (2003)

[7]

Lehto O., Univalent Functions and Teichmüller Spaces, (1987)

[8]

Schippers E., Distortion theorems for higher-order Schwarzian derivatives of univalent functions, Proc. Amer. Math. Soc., 128, 11, pp. 3241-3249, (2000)

[9]

Mejia D., Pommerenke Ch., Sobre la derivada Schwarziana de aplicaciones conformes hiperbólicamente, Rev. Colomb. Mat., 35, 2, pp. 51-60, (2001)

[10]

Schippers E., Conformal invariants and higher-order Schwarz lemmas, J. Anal. Math., 90, pp. 217-241, (2003)

← 1 2 3 →