Functional models and asymptotically orthonormal sequences
Annales de l'Institut Fourier, Volume 53 (2003) no. 5, p. 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 : https://doi.org/10.5802/aif.1987
Classification:  47A45,  46E22,  46B15,  30D55
Keywords: Hardy space, functional model, asymptotically orthornormal sequence
@article{AIF_2003__53_5_1527_0,
     author = {Chalendar, Isabelle and Fricain, Emmanuel and Timotin, Dan},
     title = {Functional models and asymptotically orthonormal sequences},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {5},
     year = {2003},
     pages = {1527-1549},
     doi = {10.5802/aif.1987},
     zbl = {1060.47014},
     mrnumber = {2032942},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_5_1527_0}
}
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. http://www.numdam.org/item/AIF_2003__53_5_1527_0/

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