On a Generalization of Fueter’s Theorem

Abstract

In this paper we discuss a generalization of Fueter’s theorem which states that whenever $f(x_0, x)$ is holomorphic in $x_0+x$, then it satisfies $D?f = 0, D= \partial_{x_0} + i \partial_{x_1}+ j \partial_{x_2} + k \partial_{x_3}$ being the Fueter operator.