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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.

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