Duality of the space of germs of harmonic vector fields on a compact

A vector field $\overline{u}$ in ${\mathbb{R}}^3$ is said to be harmonic in the open set U if $\mathrm{rot}\overline{u}=\overline{0}$, $\mathrm{div}\overline{u}=0$ in U. Harmonic vector fields are a natural extension to ${\mathbb{R}}^3$ of the concept of analytic function of complex variable. We characterize continuous linear functionals acting on the space $h(K)$ of germs of harmonic vector fields on a compact set K. This result provides an ${\mathbb{R}}^3$-analog of a theorem by G. Köthe on the dual of the space of germs of analytic functions of complex variable on a compact. To cite this article: R. Dáger, A. Presa, C. R. Acad. Sci. Paris, Ser. I 343 (2006).