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Autumn 2019 Invertibility of Toeplitz operators with polyanalytic symbols
Akaki Tikaradze
Adv. Oper. Theory 4(4): 793-801 (Autumn 2019). DOI: 10.15352/aot.1812-1451

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

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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

Information

Received: 23 December 2018; Accepted: 2 April 2019; Published: Autumn 2019
First available in Project Euclid: 15 May 2019

zbMATH: 07064106
MathSciNet: MR3949976
Digital Object Identifier: 10.15352/aot.1812-1451

Subjects:
Primary: 47B35
Secondary: ‎32A36‎, 46E22

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 4 • Autumn 2019
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