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# ECHANTILLONNAGE POUR LES ESPACESDE FONCTIONS ANALYTIQUES À POIDS

Abstract : We are interested in the sampling problem for the spaces of analytic functions in the unit disk $\DD\subset\CC$, with radial weights. We consider the Banach space
$A_h(\DD)=\{f \text{ analytic on } \DD : \|f\|_h=\sup_{z\in\DD}|f(z)|e^{-h(|z|)}<+\infty\},$
where the weight $h$ is of class $C^2$ and $h(r)\to+\infty$ as $r\to1-$.

The first chapter deals with the case of slowly increasing weights. We show that Möbius stability of sampling fails in $A_h(\DD)$.

The two following chapters deal with the case of fast increasing weights. We characterize sampling sequences for $A_h(\DD)$ in terms of density.
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https://tel.archives-ouvertes.fr/tel-00011164
Contributor : Rémi Dhuez Connect in order to contact the contributor
Submitted on : Friday, December 9, 2005 - 3:51:13 PM
Last modification on : Wednesday, October 10, 2018 - 1:26:34 AM
Long-term archiving on: : Friday, April 2, 2010 - 11:22:50 PM

### Identifiers

• HAL Id : tel-00011164, version 1

### Citation

Rémi Dhuez. ECHANTILLONNAGE POUR LES ESPACES
DE FONCTIONS ANALYTIQUES À POIDS. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2005. Français. ⟨tel-00011164⟩

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