Polyharmonicity, Almansi-type decompositions and Fueter-Sce theorem for several Clifford variables

2025/03/06 by Giulio Binosi, Binosi, Giulio
Mathematics · #30G35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2503.04329

openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study some harmonic properties of slice regular functions in one and several Clifford variables and give explicit formulas of the iterated Laplacian applied to slice regular functions and to their spherical derivative, which are new also in the one variable context. We propose several Almansi-type decompositions for slice functions in several Clifford variables. As a consequence, we establish a several variables version of Fueter-Sce theorem.

Related

• Almansi-type decomposition and Fueter-Sce theorem for generalized partial-slice regular functions
• Growth theorems in slice analysis of several variables
• Functions and operators of the polyharmonic and polyanalytic Clifford fine structures on the S-spectrum
• A manifold Fueter-Sce phenomenon in one hypercomplex variable
• Harmonic and polyanalytic functional calculi on the S-spectrum for unbounded operators