On the Fueter–Sce theorem for generalized partial-slice monogenic functions

In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both monogenic functions and slice monogenic functions with values in a Clifford algebra. In this paper, we establish a version of the Fueter–Sce theorem in this new s...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2024-09
Main Authors: Xu, Zhenghua, Sabadini, Irene
Format: Article
Language:English
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Summary:In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both monogenic functions and slice monogenic functions with values in a Clifford algebra. In this paper, we establish a version of the Fueter–Sce theorem in this new setting, which allows to construct monogenic functions in higher dimensions starting from generalized partial-slice monogenic functions. We also prove that an alternative construction can be obtained by using the dual Radon transform. It turns out that these two constructions are closely related to the generalized CK-extension.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-024-01508-1