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On the Commutativity of a Certain Class of Toeplitz Operators

Issam Louhichi; Fanilo Randriamahaleo; Lova Zakariasy — 2014

Concrete Operators

One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex place C is to completely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. Here we shall study the commutants of a certain class of quasihomogeneous Toeplitz operators defined on the harmonic Bergman space.

On the powers of quasihomogeneous Toeplitz operators

Aissa Bouhali; Zohra Bendaoud; Issam Louhichi — 2021

Czechoslovak Mathematical Journal

We present sufficient conditions for the existence of $p$ th powers of a quasihomogeneous Toeplitz operator $T_{e^{i s θ} ψ}$ , where $ψ$ is a radial polynomial function and $p$ , $s$ are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis.

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