On duality of spaces of harmonic vector fields

Details On duality of spaces of harmonic vector fields On duality of spaces of harmonic vector fields

2006-10-30

arxiv.org/abs/math/0610924v1

Mathematics

Functional Analysis

20 pages

Scientific paper

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.

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