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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.


This article was originally published in Mathematische Nachrichten in 2022.

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Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.



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