Composition operators in the Dirichlet series setting

被引:3
作者
Quefferlec, Herve [1 ]
机构
[1] Univ Lille 1, UFR Math, F-59655 Villeneuve Dascq, France
来源
PERSPECTIVES IN OPERATOR THEORY | 2007年 / 75卷
关键词
composition operators; Taylor series; Dirichlet series;
D O I
10.4064/bc75-0-16
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this work, we begin with a survey of composition operators on the Hardy space H-2 and on the Wiener algebra A(+) of absolutely convergent Taylor series, with special emphasis on their compactness, or invertibility, or isometric character. The main results are due respectively to J. Shapiro and D. Newman. In a second part, we present more recent results, due to Gordon and Hedenmalm on the one hand, and to Bayart, the author et al. on the other hand, concerning the analogues of H-2 and A+ in the setting of Dirichlet series. We are led to the intermediate study of Taylor series in several, or countably many, variables. We finish with some open problems.
引用
收藏
页码:261 / 287
页数:27
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