A vector field in is said to be harmonic in the open set U if , in U. Harmonic vector fields are a natural extension to of the concept of analytic function of complex variable. We characterize continuous linear functionals acting on the space of germs of harmonic vector fields on a compact set K. This result provides an -analog of a theorem by G. Köthe on the dual of the space of germs of analytic functions of complex variable on a compact.
On dit qu'un champ de vecteurs dans est harmonique dans un ouvert si , dans U. Les champs de vecteurs harmoniques constituent une extension naturelle dans des fonctions analitiques complexes. Nous caractérisons les functionels linéares et continues qui agissent dans l'espace des germes des champs de vecteurs harmoniques sur un compact K. Ce résultat est l'analogue dans du théorème de G. Köthe sur le dual de l'espace des germes des fonctions analytiques de variable complexe sur un compact.
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René Dáger 1; Arturo Presa 2
@article{CRMATH_2006__343_1_19_0, author = {Ren\'e D\'ager and Arturo Presa}, title = {Duality of the space of germs of harmonic vector fields on a compact}, journal = {Comptes Rendus. Math\'ematique}, pages = {19--22}, publisher = {Elsevier}, volume = {343}, number = {1}, year = {2006}, doi = {10.1016/j.crma.2006.05.002}, language = {en}, }
René Dáger; Arturo Presa. Duality of the space of germs of harmonic vector fields on a compact. Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 19-22. doi : 10.1016/j.crma.2006.05.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.05.002/
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