Title :

On approximation numbers of composition operators

Author(s) :

Li, Daniel [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Queffélec, Hervé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rodriguez-Piazza, Luis [Auteur]

English keyword(s) :

approximation number
Bergman space
Carleson measure
composition operator
Hardy space
interpolation sequence
reproducing kernel
weighted Bergman space
weighted shift

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces $\mathfrak{B}_\alpha$ of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they ...
Show more >We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces $\mathfrak{B}_\alpha$ of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bounds and explicit an example.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL