Suppose is the Hardy space of the unit disc in the complex plane, while is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.
Supposons que est l’espace de Hardy du disque unité du plan complexe et une fonction intérieure. On donne des conditions pour qu’une suite de noyaux reproduisants normalisés dans l’espace modèle soit asymptotiquement proche d’une suite orthonormale. La question de la complétude est aussi étudiée.
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
@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}, pages = {1527--1549}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {5}, year = {2003}, doi = {10.5802/aif.1987}, zbl = {1060.47014}, mrnumber = {2032942}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1987/} }
TY - JOUR AU - Chalendar, Isabelle AU - Fricain, Emmanuel AU - Timotin, Dan TI - Functional models and asymptotically orthonormal sequences JO - Annales de l'Institut Fourier PY - 2003 SP - 1527 EP - 1549 VL - 53 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1987/ DO - 10.5802/aif.1987 LA - en ID - AIF_2003__53_5_1527_0 ER -
%0 Journal Article %A Chalendar, Isabelle %A Fricain, Emmanuel %A Timotin, Dan %T Functional models and asymptotically orthonormal sequences %J Annales de l'Institut Fourier %D 2003 %P 1527-1549 %V 53 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1987/ %R 10.5802/aif.1987 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.1987/
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