Density of disk algebra functions in de Branges–Rovnyak spaces

Alexandru Aleman; Bartosz Malman

doi:10.1016/j.crma.2017.07.015

Complex analysis/Functional analysis

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]

Présenté par : the Editorial Board

Alexandru Aleman ¹ ; Bartosz Malman ¹

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.

Abstract (VO)
Résumé

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 $H^{\infty}$ . 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 $H^{\infty}$ . En utilisant aussi des théorèmes précédents, il résulte que cette classe de fonctions est dense dans un espace de Branges–Rovnyak quelconque.

Reçu le : 2017-04-21
Accepté le : 2017-07-20
Publié le : 2017-08-01

DOI : 10.1016/j.crma.2017.07.015

Affiliations des auteurs :

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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     author = {Alexandru Aleman and Bartosz Malman},
     title = {Density of disk algebra functions in de {Branges{\textendash}Rovnyak} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {871--875},
     publisher = {Elsevier},
     volume = {355},
     number = {8},
     year = {2017},
     doi = {10.1016/j.crma.2017.07.015},
     language = {en},
}

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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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