Monogenic functions taking values  in generalized Clifford algebras

Doan Cong Dinh

doi:10.37863/umzh.v73i11.1033

Doan Cong Dinh School Appl. Math. and Informatics, Hanoi Univ. Sci. and Technology, Vietnam

DOI: https://doi.org/10.37863/umzh.v73i11.1033

Keywords: Generalized Clifford algebras, ; Generalized Clifford analysis, Monogenic functions, Cauchy integral representation formula

Abstract

UDC 512.579

Generalized Clifford algebras are constructed by various methods and have some applications in mathematics and physics.
In this paper we introduce a new type of generalized Clifford algebra such that all components of a monogenic function
are solutions of an elliptic partial differential equation. One of our aims is to cover more partial differential equations in
framework of Clifford analysis. We shall prove some Cauchy integral representation formulae for monogenic functions in
those cases.

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