2014•Complex Variables and Elliptic EquationsRequires access

Cauchy-type integral formula and Plemelj formula of hypermonogenic functions on unbounded domains

Xiaoli Bian, Junxia Li, Yuying Qiao

Abstract

In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries.

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Key concepts: Mathematics, Cauchy's integral formula, Cauchy distribution, Type (biology), Bounded function, Pure mathematics, Clifford analysis, Domain (mathematical analysis)