Fock and Hardy spaces: Clifford Appell case

Daniel Alpay, Kamal Diki and Irene Sabadini

Mathematische Nachrichten, 2022, vol. 295, issue 5, 834-860

Abstract: In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions. The construction is based on a general idea which allows us to obtain various function spaces by specifying a suitable sequence of real numbers. We focus on the Fock and Hardy cases in this setting, and we study the action of the Fueter mapping and its range.

Date: 2022
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https://doi.org/10.1002/mana.202000359

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