Comptes Rendus
no. 8
Complex analysis/Functional analysis
Density of disk algebra functions in de Branges–Rovnyak spaces

Presented by: the Editorial Board

Alexandru Aleman1; Bartosz Malman1
1 Centre for Mathematical Sciences, Lund University, P.O Box 118, SE-22100 Lund, Sweden
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 871-875.

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 H∞. Together with previous theorems, it follows that this class of functions is dense in any de Branges–Rovnyak space.

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 H∞. En utilisant aussi des théorèmes précédents, il résulte que cette classe de fonctions est dense dans un espace de Branges–Rovnyak quelconque.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.07.015

Alexandru Aleman 1; Bartosz Malman 1

1 Centre for Mathematical Sciences, Lund University, P.O Box 118, SE-22100 Lund, Sweden 
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Alexandru Aleman; Bartosz Malman. Density of disk algebra functions in de Branges–Rovnyak spaces. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 871-875. doi : 10.1016/j.crma.2017.07.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.015/

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