Harmonic multivector fields and the Cauchy integral decomposition in Clifford analysis

Abstract:

In this paper we study the problem of decomposing a Hölder continuous k-grade multivector field Fk on the boundary Γ of an open bounded subset Ω in Euclidean space ℝn into a sum F k = Fk+ + Fk- of harmonic k-grade multivector fields Fk± in Ω+ = Ω and Ω- = ℝn / (Ω ∪ Γ) respectively. The necessary and sufficient conditions upon Fk we thus obtain complement those proved by Dyn'kin in [20,21] in the case where Fk is a continuous k-form on Γ. Being obtained within the framework of Clifford analysis and hence being of a pure function theoretic nature, they once more illustrate the importance of the interplay between Clifford analysis and classical real harmonic analysis.

Año de publicación:

2004

Keywords:

• Cauchy transform
• Clifford analysis
• Multivector fields

Fuente:

scopus