Duality for Harmonic Differential Forms Via Clifford Analysis

The space HFk(Ω) of harmonic multi-vector fields in a domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\Omega \subset \mathbb{R}^{n}$$ \end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbf{E} \subset \mathbb{R}^{n}$$ \end{document} 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.