Dunkl regularity over alternative $*$-algebras
Complex Variables
2026-02-03 v1
Abstract
We characterise slice-regularity of functions over a real alternative *-algebra using operators that arise in Dunkl operator theory. We present a unifying perspective on hypercomplex analysis by defining a family of function spaces in the kernel of Dunkl-Cauchy-Riemann operators. Each of these function spaces, whose elements are called Dunkl-regular functions, refines Dunkl monogenic function theory and Dunkl harmonic analysis on Euclidean spaces. This approach allows a wide variety of hypercomplex function theories to be embedded as subcases of Dunkl monogenic function theory. This paves the way for further interactions between Dunkl theory and hypercomplex analysis.
Cite
@article{arxiv.2602.01907,
title = {Dunkl regularity over alternative $*$-algebras},
author = {Giulio Binosi and Alessandro Perotti},
journal= {arXiv preprint arXiv:2602.01907},
year = {2026}
}