Abstract
In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C n+1 , so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation DΔ m f = 0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of C n+1 , deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.
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