Commuting Toeplitz operators with biharmonic symbols
Aissa Bouhali, Issam Louhichi, Abdelrahman Yousef
TL;DR
This paper characterizes when two Toeplitz operators with biharmonic symbols commute on the Bergman space, providing a full description of normal operators within this class.
Contribution
It offers a complete characterization of commuting Toeplitz operators with biharmonic symbols and describes all normal operators in this subclass.
Findings
Complete characterization of commuting Toeplitz operators with biharmonic symbols.
Full description of normal Toeplitz operators with these symbols.
Advances understanding of the structure of Toeplitz operators on Bergman space.
Abstract
We investigate the commutant problem for Toeplitz operators on the Bergman space of the unit disk whose symbols belong to a subclass of biharmonic functions. We obtain a complete characterization of when two such Toeplitz operators commute. As a consequence, we derive a full description of normal Toeplitz operators with symbols in this class.
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