[Densité des fonctions dans l'algèbre du disque dans les espaces de de Branges–Rovnyak]
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.
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.
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@article{CRMATH_2017__355_8_871_0,
author = {Aleman, Alexandru and Malman, Bartosz},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.07.015/}
}
TY - JOUR AU - Aleman, Alexandru AU - Malman, Bartosz TI - Density of disk algebra functions in de Branges–Rovnyak spaces JO - Comptes Rendus. Mathématique PY - 2017 SP - 871 EP - 875 VL - 355 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.07.015/ DO - 10.1016/j.crma.2017.07.015 LA - en ID - CRMATH_2017__355_8_871_0 ER -
%0 Journal Article %A Aleman, Alexandru %A Malman, Bartosz %T Density of disk algebra functions in de Branges–Rovnyak spaces %J Comptes Rendus. Mathématique %D 2017 %P 871-875 %V 355 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.07.015/ %R 10.1016/j.crma.2017.07.015 %G en %F CRMATH_2017__355_8_871_0
Aleman, Alexandru; Malman, Bartosz. Density of disk algebra functions in de Branges–Rovnyak spaces. Comptes Rendus. Mathématique, Tome 355 (2017) no. 8, pp. 871-875. doi : 10.1016/j.crma.2017.07.015. http://www.numdam.org/articles/10.1016/j.crma.2017.07.015/
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