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arXiv · 2607.19496

A connection between quaternionic slice regular and Fueter hyperholormorphic functions

José Oscar González-Cervantes·Daniel González-Campos·Juan Bory-Reyes·Baruch Schneider
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Abstract

This paper presents some results for the slice regular functions and hyperholomorphic functions theories, as consequences of new relationships between the global operator $G$, Fueter operator $\mathcal D$ and Laplacian operator $\Delta_{\mathbb{R}^{4}}$. Although our results are presented in the quaternionic setting, a fine interpretation in terms of vector calculus of the slice regular function theory yields an interesting relationship between this theory and harmonic analysis. Moreover, we introduce and study a submodule of the hyperholomorphic functions associated to the unit ball $\mathbb B^4(0,1)$ given in terms of new series expansions of the functions.

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José Oscar González-Cervantes, Daniel González-Campos, Juan Bory-Reyes, Baruch Schneider. 2026-07-21. A connection between quaternionic slice regular and Fueter hyperholormorphic functions. https://arxiv.org/abs/2607.19496

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