Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772332 | Journal of Functional Analysis | 2017 | 42 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hui Dan, Kunyu Guo, Hansong Huang,