Isometries of the Dirichlet space among the composition operators

被引：27
|
作者：
Martín, MJ [1 ]
Vukotic, D
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：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 06期
关键词：
D O I：
10.1090/S0002-9939-05-08182-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that every composition operator which is an isometry of the Dirichlet space is induced by a univalent full map of the disk into itself that fixes the origin. This is an analogue of the Hardy space result for inner functions due to Nordgren. The proof relies on the Stone-Weierstrass theorem and the Riesz representation theorem.
引用
收藏
页码：1701 / 1705
页数：5
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