Functional models and asymptotically orthonormal sequences
[Modèles fonctionnels et suites asymptotiquement orthonormales]
Chalendar, Isabelle ; Fricain, Emmanuel ; Timotin, Dan
Annales de l'Institut Fourier, Tome 53 (2003), p. 1527-1549 / Harvested from Numdam
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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.

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.

Publié le : 2003-01-01
DOI : https://doi.org/10.5802/aif.1987
Classification:  47A45,  46E22,  46B15,  30D55
Mots clés: espace de Hardy, modèle fonctionnel, suite asymptotiquement orthonormale 
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     title = {Functional models and asymptotically orthonormal sequences},
     journal = {Annales de l'Institut Fourier},
     volume = {53},
     year = {2003},
     pages = {1527-1549},
     doi = {10.5802/aif.1987},
     mrnumber = {2032942},
     zbl = {1060.47014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2003__53_5_1527_0}
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Chalendar, Isabelle; Fricain, Emmanuel; Timotin, Dan. Functional models and asymptotically orthonormal sequences. Annales de l'Institut Fourier, Tome 53 (2003) pp. 1527-1549. doi : 10.5802/aif.1987. http://gdmltest.u-ga.fr/item/AIF_2003__53_5_1527_0/

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