文献类型：期刊文献

英文题名：Analytic Toeplitz Operators, Distinguished Varieties and Boundary Behavior of Symbols

作者：Dan, Hui[1];Guo, Kunyu[1];Huang, Hansong[2]

机构：[1]Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2019

卷号：91

期号：5

外文期刊名：INTEGRAL EQUATIONS AND OPERATOR THEORY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000488948200001)】；

基金：This work is supported by the National Natural Science Foundation of China.

语种：英文

外文关键词：The totally Abelian property; Finite Blaschke products; Distinguished varieties

摘要：Based on our paper (Dan et al. in J Funct Anal 273:559-597, 2017), we continue the study on totally Abelian analytic Toeplitz operators on the Hardy space. However, rather than to focus on the geometry of the symbol curves associated with these operators as done before, this paper is to consider the Riemann surfaces in C-2 defined by these symbols. In this way, we reveal the connection between the totally Abelian property of these operators and the distinguished varieties arising from the Riemann surfaces, thus widely extend the classes of function symbols considered in the previous paper. Furthermore, an alternative method is used to provide a sharp characterization for analytic Toeplitz operators being not totally Abelian.