文献类型：期刊文献

英文题名：Totally Abelian Toeplitz operators and geometric invariants associated with their symbol curves

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：2017

卷号：273

期号：2

起止页码：559

外文期刊名：JOURNAL OF FUNCTIONAL ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000402449600003)】；

基金：This work is partially supported by National Natural Science Foundation of China (grant number: 11371096, 11471113), and by Shanghai Center for Mathematical Sciences. The authors thank Professor D. Zheng a lot for communications. They are also heartly grateful to the referee for valuable suggestions on the manuscript of this paper, which makes it more readable.

语种：英文

外文关键词：Local inverse; Winding numbers; Multiplicities of self-intersection; Meromorphic functions

摘要：This paper mainly studies totally Abelian operators in the context of analytic Toeplitz operators on both the Hardy and Bergman space. When the symbol is a meromorphic function on C, we establish the connection between the totally Abelian property of these operators and geometric properties of their symbol curves. It is found that winding numbers and multiplicities of self-intersection of symbol curves play an important role in this topic. Techniques of group theory, complex analysis, geometry and operator theory are intrinsic in this paper. As a byproduct, under a mild condition we provide an affirmative answer to a question raised in [2], and also construct some examples to show that the answer is negative if the associated conditions are weakened. (C) 2017 Elsevier Inc. All rights reserved.