Duality for Harmonic Differential Forms Via Clifford Analysis

Abstract

The space HFk(Ω) of harmonic multi-vector fields in a domain \(\Omega \subset \mathbb{R}^{n}\) as introduced in [1] is closely connected to the space of harmonic forms. The main aim of this paper is to characterize the dual space of HFk(E) being \(\mathbf{E} \subset \mathbb{R}^{n}\) a compact set. It is proved that HFk(E)* is isomorphic to a certain quotient space of so-called harmonic pairs outside E vanishing at infinity.