Iterated generalized dirac operators of mixed sides

In the development of the theories of generalized monogenic functions in Clifford analysis, there are natural appearances of the composition of the Dirac operators such as polymonogenic function, inframonogenic function, infrapolymonogenic functions, iterated ( α , β ) -Dirac operators, ( φ , ψ ) -h...

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Bibliographic Details
Published in:Boletín de la Sociedad Matemática Mexicana 2024-03, Vol.30 (1), Article 23
Main Author: Dinh, Doan Cong
Format: Article
Language:English
Subjects:
Harmonic functions
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Article
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Summary:In the development of the theories of generalized monogenic functions in Clifford analysis, there are natural appearances of the composition of the Dirac operators such as polymonogenic function, inframonogenic function, infrapolymonogenic functions, iterated ( α , β ) -Dirac operators, ( φ , ψ ) -harmonic functions, ( φ , ψ ) -inframonogenic functions, iterated generalized Dirac operators associated to different structural sets. In this paper, we introduce a class of iterated generalized Dirac operators of mixed sides which is a generalization of those theories. By using the endomorphisms on Clifford algebras, we construct the Borel–Pompeiu formula respect to these operators.
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-024-00603-w