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On the powers of quasihomogeneous Toeplitz operators

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Abstract

We present sufficient conditions for the existence of pth powers of a quasiho-mogeneous Toeplitz operator Teiφ, where φ 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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Acknowledgments

The authors are grateful to the referee for his/her excellent suggestions. The third author would also like to give a heartfelt thanks to R. Duduchava (private communication, 2020) for valuable discussions regarding the Mellin transform.

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Correspondence to Issam Louhichi.

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Bouhali, A., Bendaoud, Z. & Louhichi, I. On the powers of quasihomogeneous Toeplitz operators. Czech Math J 71, 1049–1061 (2021). https://doi.org/10.21136/CMJ.2021.0193-20

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  • DOI: https://doi.org/10.21136/CMJ.2021.0193-20

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