2011•Complex Variables and Elliptic EquationsRequires access

Poincaré–Bertrand transformation formula of Cauchy-type singular integrals in Clifford analysis

Yuying Qiao, Yongzhi Steve Xu, Heju Yang

Abstract

This article studies the Poincaré–Bertrand transformation formula of Cauchy-type singular integrals of double multi-variables Clifford functions. First, it discusses some properties for several singular integrals about Clifford functions, and then proves the existence, for Cauchy principal value, of some Cauchy-type singular integrals with a parameter. Finally, it confirms the Poincaré–Bertrand transformation formula.

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Key concepts: Mathematics, Cauchy principal value, Cauchy's integral theorem, Clifford analysis, Cauchy's integral formula, Cauchy distribution, Singular integral, Residue theorem