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Cauchy–Pompeiu formula for multi-meta-weighted-monogenic functions of first class

Abstract:

In this paper we give a Cauchy–Pompeiu type integral formula for a class of functions called multi-meta-weighted-monogenic using a distance calculated via the quadratic form associated with an elliptic operator. This is used for the construction of the kernel over the domain Rm+1, constructed by fixing the real part for all products of ℝm+1 = ℝm1 × ℝm2 ×· · ·×ℝmn. Also, we present a section where we discuss the inhomogeneous meta-nweighted- monogenic equation and a distributional solution for this equation is obtained. In some special cases, the distributional solution becomes a classical solution.