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Comptes Rendus Mathématique
Volume 355, n° 8
pages 871-875 (août 2017)
Doi : 10.1016/j.crma.2017.07.015
Received : 21 April 2017 ;  accepted : 20 July 2017
Density of disk algebra functions in de Branges–Rovnyak spaces
Densité des fonctions dans l'algèbre du disque dans les espaces de de Branges–Rovnyak
 

Alexandru Aleman , Bartosz Malman
 Centre for Mathematical Sciences, Lund University, P.O Box 118, SE-22100 Lund, Sweden 

Abstract

We prove that functions analytic in the unit disk and continuous up to the boundary are dense in the de Branges–Rovnyak spaces induced by the extreme points of the unit ball of  . Together with previous theorems, it follows that this class of functions is dense in any de Branges–Rovnyak space.

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

On démontre que les fonctions analytiques dans le disque unité et continues dans le disque fermé sont denses dans l'espace de Branges–Rovnyak généré par un point extrémal de la boule unité de  . En utilisant aussi des théorèmes précédents, il résulte que cette classe de fonctions est dense dans un espace de Branges–Rovnyak quelconque.

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


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