Norms and spectral radii of composition operators acting on the Dirichlet space

被引：18

作者：

Martín, MJ

Vukotic, D ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Univ Carlos III Madrid, Dept Econ, E-28903 Getafe, Madrid, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2005年 / 304卷 / 01期

关键词：

Dirichlet space; composition operator; operator norm; spectral radius; hyperbolic metric;

D O I：

10.1016/j.jmaa.2004.09.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain new upper bounds on the norms of univalently induced composition operators acting on the Dirichlet space and compute explicitly the norms for univalent symbols whose range is the disk minus a set of measure zero. As an application, we show that the spectral radius of every univalently induced composition operator on the Dirichlet space is equal to one. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：22 / 32

页数：11

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