广义Segal-Bargmann空间上无界Toeplitz算子的交换

王晓峰, 夏锦, 陈建军

数学学报 ›› 2019, Vol. 62 ›› Issue (3) : 409-426.

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数学学报 ›› 2019, Vol. 62 ›› Issue (3) : 409-426. DOI: 10.12386/A2019sxxb0039
论文

广义Segal-Bargmann空间上无界Toeplitz算子的交换

    王晓峰1, 夏锦1, 陈建军2,3
作者信息 +

Commuting Toeplitz Operators and Toeplitz Operators with Unbounded Symbols on Generalized Segal-Bargmann Space

    Xiao Feng WANG1, Jin XIA1, Jian Jun CHEN2,3
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文章历史 +

摘要

本文给出了复平面C上广义Fock空间中两个Toeplitz算子TuTv的性质.假设u是一个径向函数,两算子是可交换的.在一定的增长条件之下,我们证明出v也是一个径向函数.最后还构造了一个具有本性无界符号的Sp紧Toeplitz算子.

Abstract

We consider two Toeplitz operators Tu and Tv on the generalized Fock space over the complex plane C. Let's assume that u is a radial function and the two operators commute. Under certain growth condition at infinity of u and v, we prove that v must be a radial function as well. Finally, we also construct a Sp class of Toeplitz operators on the generalized Fock space with symbols which are essentially unbounded on any point of the complex plane C.

关键词

Fock空间 / 交换Toeplitz算子 / Sp

Key words

Fock space / commuting Toeplitz operator / Sp class

引用本文

导出引用
王晓峰, 夏锦, 陈建军. 广义Segal-Bargmann空间上无界Toeplitz算子的交换. 数学学报, 2019, 62(3): 409-426 https://doi.org/10.12386/A2019sxxb0039
Xiao Feng WANG, Jin XIA, Jian Jun CHEN. Commuting Toeplitz Operators and Toeplitz Operators with Unbounded Symbols on Generalized Segal-Bargmann Space. Acta Mathematica Sinica, Chinese Series, 2019, 62(3): 409-426 https://doi.org/10.12386/A2019sxxb0039

参考文献

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基金

国家自然科学基金(11471084;11301101);广东省青年创新人才项目(2017KQNCX220);肇庆学院校级课题项目(201732);肇庆学院博士启动项目(221622)

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