Title :

Constructive approximation in de Branges-Rovnyak spaces

Author(s) :

El-Fallah, O [Auteur]
Fricain, E [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Kellay, Karim [Auteur]
Institut de Mathématiques de Bordeaux [IMB]
Mashreghi, J [Auteur]
Ransford, T. [Auteur]

Journal title :

Constructive Approximation

Pages :

269-281

Publisher :

Springer Verlag

Publication date :

2016-09-21

ISSN :

0176-4276

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]
Mathématiques [math]/Variables complexes [math.CV]
Mathématiques [math]/Analyse classique [math.CA]

English abstract : [en]

In most classical holomorphic function spaces on the unit disk, a function $f$ can be approximated in the norm of the space by its dilates $f_r(z):=f(rz)~(r < 1)$.We show that this is \emph{not} the case for the de ...
Show more >In most classical holomorphic function spaces on the unit disk, a function $f$ can be approximated in the norm of the space by its dilates $f_r(z):=f(rz)~(r < 1)$.We show that this is \emph{not} the case for the de Branges--Rovnyak spaces $\cH(b)$. More precisely, we give an example of a non-extreme point $b$ of the unit ball of $H^\infty$ and a function $f\in\cH(b)$ such that $\lim_{r\to1^-}\|f_r\|_{\cH(b)}=\infty$.It is known that, if $b$ is a non-extreme point of the unit ball of $H^\infty$, then polynomials are dense in $\cH(b)$. We give the first constructive proof of this fact.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL