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Duality for harmonic differential forms via Clifford analysis. (English) Zbl 1134.30336
Summary: The space \(HF_k(\Omega )\) of harmonic multi-vector fields in a domain \(\Omega \subset \mathbb{R}^{n}\) as introduced by R. Abreu-Blaya et al. [Bull. Belg. Math. Soc. - Simon Stevin 11, No. 1, 95–110 (2004; Zbl 1063.30045)] 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 \(\mathbf{E} \subset \mathbb{R}^{n}\) 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.

30G35 Functions of hypercomplex variables and generalized variables
58A10 Differential forms in global analysis
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