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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Veröffentlicht in:Annali di matematica pura ed applicata Jg. 204; H. 2; S. 835 - 857
Hauptverfasser: Xu, Zhenghua, Sabadini, Irene
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2025
Springer Nature B.V
Schlagworte:
Mathematics
Mathematics and Statistics
Radon transformation
Theorems
Slice monogenic functions
Clifford algebras
Functions of a hypercomplex variable
Secondary: 32A30
Primary: 30G35
Monogenic functions
ISSN:0373-3114, 1618-1891
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-024-01508-1