no. 5
Functional models and asymptotically orthonormal sequences
[Modèles fonctionnels et suites asymptotiquement orthonormales]
Chalendar, Isabelle1 ; Fricain, Emmanuel1 ; Timotin, Dan2
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)
Annales de l'Institut Fourier, Tome 53 (2003) no. 5, pp. 1527-1549.

Supposons que H2 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 KΘ=H2⊖ΘH2 soit asymptotiquement proche d’une suite orthonormale. La question de la complétude est aussi étudiée.

Suppose H2 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 KΘ=H2⊖ΘH2 to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.

DOI : 10.5802/aif.1987
Classification : 47A45, 46E22, 46B15, 30D55
Keywords: Hardy space, functional model, asymptotically orthornormal sequence
Mots-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, Tome 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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