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Comptes Rendus Mathématique
Volume 343, n° 1
pages 19-22 (juillet 2006)
Doi : 10.1016/j.crma.2006.05.002
Received : 8 April 2006 ;  accepted : 2 May 2006
Duality of the space of germs of harmonic vector fields on a compact
Dualité de lʼespace des germes des champs de vecteurs harmoniques sur un compact
 

René Dáger a , Arturo Presa b
a Departamento de Matemática Aplicada, Universidad Complutense, 28040 Madrid, Spain 
b Mathematics Department, Miami Dade College, Wolfson Campus, Miami, FL 33132-2296, USA 

Abstract

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. To cite this article: R. Dáger, A. Presa, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Résumé

On dit quʼun 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 lʼespace   des germes des champs de vecteurs harmoniques sur un compact K . Ce résultat est lʼanalogue dans   du théorème de G. Köthe sur le dual de lʼespace des germes des fonctions analytiques de variable complexe sur un compact. Pour citer cet article : R. Dáger, A. Presa, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.


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