English

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.

Keywords

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

R2 v1 2026-07-22T17:45:18.048Z