Almansi-type decomposition and Fueter-Sce theorem for generalized partial-slice regular functions

TL;DR

This paper extends classical function theories by introducing Almansi-type decompositions and Fueter-Sce theorem enhancements for generalized partial-slice regular functions within Clifford algebras, unifying monogenic and slice monogenic functions.

Contribution

It provides two new Almansi decompositions and two improved Fueter-Sce theorems for the generalized partial-slice regular functions, advancing the mathematical framework.

Findings

Two Almansi-type decompositions established

Enhanced Fueter-Sce theorems derived for the new setting

Unified approach to monogenic and slice monogenic functions

Abstract

Very recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced to unify the theory of monogenic functions and of slice monogenic functions over Clifford algebras. Inspired by the work of A. Perotti, in this paper we provide two analogous versions of the Almansi decomposition in this new setting. Additionally, two enhancements of the Fueter-Sce theorem have been obtained for generalized partial-slice regular functions.