Toeplitz operators on Bergman spaces of polyanalytic functions
Zeljko Cuckovic, Trieu Le
TL;DR
This paper investigates algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions, focusing on finite-rank commutators and semi-commutators with harmonic symbols, and discusses open questions.
Contribution
It provides new results on the algebraic structure of Toeplitz operators in polyanalytic Bergman spaces, including finite-rank commutator characterizations.
Findings
Finite-rank commutators characterized
Semi-commutators analyzed for harmonic symbols
Open questions on algebraic properties raised
Abstract
We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise and discuss some open questions.
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