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A Cauchy Integral Formula for Inframonogenic Functions in Clifford Analysis

Abstract:

In this paper we derive a Cauchy integral representation formula for the solutions of the sandwich equation ∂x̲f∂x̲=0, where ∂x̲ stands for the first-order vector-valued rotation invariant differential operator in the Euclidean space Rm, called Dirac operator. Such a solutions are referred in the literature as inframonogenic functions and represent an extension of the monogenic functions, i.e., null solutions of ∂x̲, which represent higher-dimensional generalizations of the classic Cauchy–Riemann operator.