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arXiv · 2401.00620

A Borel-Pompeiu formula in a $(q,q')$-model of quaternionic analysis

José Oscar González-Cervantes·Juan Bory-Reyes·Irene Sabadini
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Abstract

The study of $\psi-$hyperholomorphic functions defined on domains in $\mathbb R^4$ with values in $\mathbb H$, namely null-solutions of the $\psi-$Fueter operator, is a topic which captured great interest in quaternionic analysis. This class of functions is more general than that of Fueter regular functions. In the setting of $(q,q')-$calculus, also known as post quantum calculus, we introduce a deformation of the $\psi-$Fueter operator written in terms of suitable difference operators, which reduces to a deformed $q$ calculus when $q'=1$. We also prove the Stokes and Borel-Pompeiu formulas in this context. This work is the first investigation of results in quaternionic analysis in the setting of the $(q,q')-$calculus theory.

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José Oscar González-Cervantes, Juan Bory-Reyes, Irene Sabadini. 2024-01-01. A Borel-Pompeiu formula in a $(q,q')$-model of quaternionic analysis. https://arxiv.org/abs/2401.00620

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