Functional models and asymptotically orthonormal sequences
Annales de l'Institut Fourier, Volume 53 (2003) no. 5, pp. 1527-1549.

Suppose H 2 is the Hardy space of the unit disc in the complex plane, while Θ is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space K Θ =H 2 ΘH 2 to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.

Supposons que H 2 est l’espace de Hardy du disque unité du plan complexe et Θ une fonction intérieure. On donne des conditions pour qu’une suite de noyaux reproduisants normalisés dans l’espace modèle K Θ =H 2 ΘH 2 soit asymptotiquement proche d’une suite orthonormale. La question de la complétude est aussi étudiée.

DOI: 10.5802/aif.1987
Classification: 47A45, 46E22, 46B15, 30D55
Keywords: Hardy space, functional model, asymptotically orthornormal sequence
Mot clés : espace de Hardy, modèle fonctionnel, suite asymptotiquement orthonormale
Chalendar, Isabelle 1; Fricain, Emmanuel 1; Timotin, Dan 2

1 Université Claude Bernard Lyon I, Institut Girard Desargues, UFR de Mathématiques, 69622 Villeurbanne Cedex (France)
2 Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest 70700 (Romania)
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Chalendar, Isabelle; Fricain, Emmanuel; Timotin, Dan. Functional models and asymptotically orthonormal sequences. Annales de l'Institut Fourier, Volume 53 (2003) no. 5, pp. 1527-1549. doi : 10.5802/aif.1987. https://aif.centre-mersenne.org/articles/10.5802/aif.1987/

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