First approach to a (q,q')-model of quaternionic analysis

The study of $\Psi$-hyperholomorphic functions defined on domains in $\mathbb R^4$ with values in $\mathbb H$, namely the null-solutions of the $\Psi$-Fueter operator, where $\Psi$ denotes a structural set, is a topic which captured great interest in quaternionic analysis. This class of functions is more general than that of Fueter regular functions. Applications of q-calculus have been investigated intensively, especially for the connections with physics. Inspired by these applications, many researchers developed the (q,q')-model (also called post quantum calculus), which is used efficiently in various areas of mathematics and also in quantum physics. The goal of the talk is to show how look, in the framework of (q,q')-calculus, a deformation of the $\Psi$-Fueter operator written in terms of suitable difference operators, which reduces to the Jackson q-derivative when q'=1. The talk is based on a joint work with José Oscar González Cervantes and Irene Sabadini.