  A differential form defined on a Riemannian manifold is said to harmonic if
it is closed and co-closed. Harmonic differential forms are a natural
multi-dimensional extension of the concept of analytic function of complex
variable. In this paper we characterize continuous linear functionals acting of
the space of germs of harmonic differential forms on a compact set. This result
provides a multi-dimensional analog of a theorem by G. K\"othe on the dual of
the space of germs of analytic functions of complex variables on a compact.
