多圆盘Bergman空间上Toeplitz算子的乘积和交换性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 304-314.

多圆盘Bergman空间上Toeplitz算子的乘积和交换性

孙志玲()

^{内蒙古民族大学数学学院内蒙古通辽 028000}

收稿日期:2018-05-21 出版日期:2020-04-26 发布日期:2020-05-21
作者简介:孙志玲, E-mail:zlingsun@126.com
基金资助:
内蒙古自治区自然科学基金(2014BS0106);内蒙古自治区自然科学基金(2016MS0118);内蒙古民族大学科学研究基金项目(NMDYB19058)

Products and Commuting of Toeplitz Operators on the Bergman Space of the Polydisk

Zhiling Sun()

^{College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia Tongliao 028000}

Received:2018-05-21 Online:2020-04-26 Published:2020-05-21
Supported by:
the NSF of Inner Mongolia(2014BS0106);the NSF of Inner Mongolia(2016MS0118);the Foundation of Inner Mongolia University for Nationalities(NMDYB19058)

摘要/Abstract

摘要：

该文给出了多圆盘Bergman空间上两个带有某种符号的Toeplitz算子的乘积等于另一个Toeplitz算子的充分必要条件，并且给出了乘积算子所带符号的公式.接下来，相应的研究了它的交换性.这些研究结果都是根据符号函数的Mellin变换.

关键词: Toeplitz算子, 多圆盘Bergman空间, Mellin变换

Abstract:

In this paper, we give some necessary and sufficient conditions for the product of two Toeplitz operators with certain symbols to be a Toeplitz operator and give a formula for the symbol of the product on the Bergman space of polydisk. Next, the corresponding commuting problem of Toeplitz operator is studied. All the results are stated in terms of the Mellin transform of the symbol.

Key words: Toeplitz operators, Bergman space of polydisk, Mellin transform

中图分类号:

O177.1

孙志玲. 多圆盘Bergman空间上Toeplitz算子的乘积和交换性[J]. 数学物理学报, 2020, 40(2): 304-314.

Zhiling Sun. Products and Commuting of Toeplitz Operators on the Bergman Space of the Polydisk[J]. Acta mathematica scientia,Series A, 2020, 40(2): 304-314.

参考文献 8

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