Fueter's theorem in discrete Clifford analysis

Abstract

In this paper, we discretize techniques for the construction of axially monogenic functions to the setting of discrete Clifford analysis. Wherefore, we work in the discrete Hermitian Clifford setting, where each basis vector ej is split into a forward and backward basis vector: . We prove a discrete version of Fueter's theorem in odd dimension by showing that for a discrete monogenic function f(ξ0,ξ1) left‐monogenic in two variables ξ0 and ξ1 and for a left‐monogenic Pk(ξ), the m‐dimensional function is in itself left monogenic, that is, a discrete function in the kernel of the discrete Dirac operator. Closely related, we consider a Vekua‐type system for the construction of axially monogenic functions. We consider some explicit examples: the discrete axial‐exponential functions and the discrete Clifford–Hermite polynomials. Copyright © 2015 John Wiley & Sons, Ltd.