Fueter's theorem for monogenic functions in biaxial symmetric domains

TL;DR

This paper extends Fueter's theorem to monogenic functions within biaxially symmetric domains, broadening the mathematical framework for analyzing such functions using advanced calculus and representation theory.

Contribution

It generalizes previous results to biaxial symmetry cases, combining direct calculus methods with representation theory for monogenic functions.

Findings

Generalized Fueter's theorem to biaxial symmetric domains

Developed a direct calculus approach for monogenic functions

Connected representation theory with explicit calculus methods

Abstract

In this paper we generalize the result on Fueter's theorem from [10] by Eelbode et al. to the case of monogenic functions in biaxially symmetric domains. To obtain this result, Eelbode et al. used representation theory methods but their result also follows from a direct calculus we established in our paper [21]. In this paper we first generalize [21] to the biaxial case and derive the main result from that.