Dunkl approach to slice regular functions

Abstract: In this paper, we show that a Clifford algebra valued function is slice if and only if it is in the kernel of Dunkl-spherical Dirac operator and a slice function $f$ is slice regular if and only if it is in the kernel of the Dunkl-Cauchy-Riemann operator of a certain parameter. Based on this observation and the inverse Dunkl intertwining operator, we present a new approach to construct a family of classical monogenic functions from a given holomorphic function.