Weighted composition operators on the Fock space

被引：5

作者：

Han, Kaikai ^{[1
]}

Wang, Maofa ^{[2
]}

机构：

[1] Hebei Univ Econ & Business, Sch Math & Stat, Shijiazhuang 050061, Hebei, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2022年 / 65卷 / 01期

基金：

中国国家自然科学基金;

关键词：

weighted composition operator; Fock space; complex symmetry; cyclicity; frame; mean ergodicity; SYMMETRIC COMPOSITION OPERATORS; COMPLEX SYMMETRY;

D O I：

10.1007/s11425-020-1752-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study weighted composition operators on the Fock space F-2. We prove that each bounded composition operator on F-2 is complex symmetric. This is in sharp contrast with the phenomenon on the Hardy space H-2(D). We characterize Hermitian weighted composition operators and algebraic weighted composition operators with degree less than or equal to two on F-2. In addition, we investigate cyclicity and hypercyclicity of complex symmetric weighted composition operators. We also characterize those weighted composition operators that preserve frames, tight frames or normalized tight frames on F-2. Finally, we study mean ergodicity and uniformly mean ergodicity of weighted composition operators.

引用

页码：111 / 126

页数：16

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