Fueter's theorem: the saga continues

Abstract

In this paper is extended the original theorem by Fueter-Sce (assigning an ${\mathbb{R}}_{0,m}$-valued monogenic function to a $\mathbb{C}$-valued holomorphic function) to the higher order case. We use this result to prove Fueter's theorem with an extra monogenic factor $P_k(x_0,\underline{x})$.

11 pages, accepted for publication in Journal of Mathematical Analysis and Applications

References in corpus (1)

• Analytic cliffordian functions

Cited by in corpus (10)

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• On a sequence of monogenic polynomials satisfying the Appell condition whose first term is a non-constant function
• Generating functions of orthogonal polynomials in higher dimensions
• Biaxial monogenic functions from Funk-Hecke's formula combined with Fueter's theorem
• Fueter's theorem for monogenic functions in biaxial symmetric domains
• A manifold Fueter-Sce phenomenon in one hypercomplex variable
• A Generalization of Fueter's Theorem in Dunkl-Clifford Analysis
• Fueter's theorem for the biregular functions of Clifford analysis
• Vekua-type systems related to two-sided monogenic functions
• A new integral formula for the inverse Fueter mapping theorem