Czechoslovak Mathematical Journal, Vol. 71, No. 4, pp. 1049-1061, 2021
On the powers of quasihomogeneous Toeplitz operators
Aissa Bouhali, Zohra Bendaoud, Issam Louhichi
Received May 13, 2020. Published online June 30, 2021.
Abstract: We present sufficient conditions for the existence of $p$th powers of a quasihomogeneous Toeplitz operator $T_{{\rm e}^{{\rm i} s\theta}\psi}$, where $\psi$ 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.
Affiliations: Aissa Bouhali, Laboratory of Pure and Applied Mathematics, Mohamed Khider University of Biskra, BP 145 RP, Biskra, Algeria, e-mail: aissa.bouhali@ens-lagh.dz; Zohra Bendaoud, Laboratory of Pure and Applied Mathematics, École Normale Supérieure of Laghouat, Trans-Sahara Hwy Laghouat, 04033 Laghouat, Algeria, e-mail: zbendaoud@gmail.com; Issam Louhichi (corresponding author), Department of Mathematics and Statistics, College of Arts and Sciences, American University of Sharjah, P.O.Box 26666, Sharjah, United Arab Emirates, e-mail: ilouhichi@aus.edu