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A Cauchy Transform for Polymonogenic Functions on Fractal Domains

Abstract:

A Cauchy integral representation formula for polymonogenic functions has been established in smoothly bounded domains, but the method by which it has been obtained cannot be extended to the case of domains with fractal boundary. In this paper an alternative polymonogenic Cauchy transform is defined, which enables us to obtain several types of integral representation formulae, including the Cauchy and Borel-Pompeiu representations in this very general geometric setting.