Duality for Harmonic Differential Forms Via Clifford Analysis

The space HF _k (Ω) of harmonic multi-vector fields in a domain 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 HF _k (E) being a compact set. It is proved that HF _k (E)^* is isomorphic to a certain quotient space of so-called harmonic pairs outside E vanishing at infinity. Research of the third author was supported by the FWO Research Network WO. 003. 01N, research of the fourth author was supported by the FWO “Krediet aan Navorsers: 1.5.106.02”