Generalized Partial-Slice Monogenic Functions: A Synthesis of Two Function Theories

In this paper, we review the notion of generalized partial-slice monogenic functions that was introduced by the authors in Xu and Sabadini (Generalized partial-slice monogenic functions, arXiv:2309.03698 , 2023). The class of these functions includes both the theory of monogenic functions and of sli...

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Veröffentlicht in:Advances in applied Clifford algebras Jg. 34; H. 2; S. 10
Hauptverfasser: Xu, Zhenghua, Sabadini, Irene
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.04.2024
Springer Nature B.V
Schlagworte:
Algebra
Applications of Mathematics
Euclidean space
Mathematical and Computational Physics
Mathematical Methods in Physics
Operators (mathematics)
Physics
Physics and Astronomy
Smoothness
Synthesis
Theoretical
Primary 30G35
Secondary 32A30
Slice monogenic functions
Clifford algebras
Functions of a hypercomplex variable
Monogenic functions
ISSN:0188-7009, 1661-4909
Online-Zugang:Volltext
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Zusammenfassung:In this paper, we review the notion of generalized partial-slice monogenic functions that was introduced by the authors in Xu and Sabadini (Generalized partial-slice monogenic functions, arXiv:2309.03698 , 2023). The class of these functions includes both the theory of monogenic functions and of slice monogenic functions over Clifford algebras and it is obtained via a synthesis operator which combines a generalized Cauchy–Riemann operator with an operator acting on slices. Besides recalling the fundamental features, we provide a notion of ∗ -product based on the CK-extension and discuss the smoothness of generalized partial-slice functions.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-024-01314-1