Abstract
We recall the algebra of endomorphisms on the so-called radial algebra of abstract vector variables which generalizes both polynomial and Clifford algebras, and the defining building blocks of a function theory in this abstract framework. These building blocks are given by the abstract versions of the Dirac operator and the directional derivatives. Together with other fundamental endomorphisms, they lead to an algebraic structure which can be considered as the abstract equivalent of orthogonal Clifford analysis. Following a similar approach, we present the axiomatic definitions of the Hermitian radial algebra, leading to the abstract equivalent of Hermitian Clifford analysis.
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