On duality of spaces of harmonic vector fields
Functional Analysis
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0610924,
title = {On duality of spaces of harmonic vector fields},
author = {René Dáger and Arturo Presa},
journal= {arXiv preprint arXiv:math/0610924},
year = {2007}
}
Comments
20 pages