Functional models and asymptotically orthonormal sequences

Chalendar, Isabelle; Fricain, Emmanuel; Timotin, Dan

doi:10.5802/aif.1987

Functional models and asymptotically orthonormal sequences
[Modèles fonctionnels et suites asymptotiquement orthonormales]

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)

Annales de l'Institut Fourier, Tome 53 (2003) no. 5, pp. 1527-1549.

Résumé
Abstract

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 $K_{Θ} = H^{2} ⊖ Θ H^{2}$ soit asymptotiquement proche d’une suite orthonormale. La question de la complétude est aussi étudiée.

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 $K_{Θ} = H^{2} ⊖ Θ H^{2}$ to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.

MR Zbl

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

Affiliations des auteurs :

Chalendar, Isabelle ¹ ; Fricain, Emmanuel ¹ ; Timotin, Dan ²

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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. http://www.numdam.org/articles/10.5802/aif.1987/

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