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arXiv · 2407.06811

Dunkl approach to slice regular functions

Giulio Binosi·Hendrik De Bie·Pan Lian
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Abstract

In this paper, we establish a connection between Dunkl analysis and slice analysis in the setting of Clifford algebras. Specifically, we show that a Clifford algebra-valued function is slice if, and only if, it belongs to the kernel of the Dunkl-spherical Dirac operator and that a slice function is slice regular if, and only if, it lies in the kernel of the Dunkl-Cauchy-Riemann operator for a suitable parameter. Based on this correspondence and the inverse Dunkl intertwining operator, we propose a new method to construct a family of classical monogenic functions from a given holomorphic function, in the spirit of Fueter theorem.

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Giulio Binosi, Hendrik De Bie, Pan Lian. 2024-07-09. Dunkl approach to slice regular functions. https://doi.org/10.1007/s10231-025-01572-1

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