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

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.