Abstract
For a class of continuous functions including complex polynomials in $z$ and $\bar{z},$ we show that the corresponding Toeplitz operator on the Bergman space of the unit disk can be expressed as a quotient of certain differential operators with holomorphic coefficients. This enables us to obtain several nontrivial operator theoretic results about such Toeplitz operators, including a new criterion for invertibility of a Toeplitz operator for a class of harmonic symbols.
Citation
Akaki Tikaradze. "Invertibility of Toeplitz operators with polyanalytic symbols." Adv. Oper. Theory 4 (4) 793 - 801, Autumn 2019. https://doi.org/10.15352/aot.1812-1451
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