Stability of the bases and frames reproducing kernels in model spaces
Annales de l'Institut Fourier, Volume 55 (2005) no. 7, pp. 2399-2422.

We study the bases and frames of reproducing kernels in the model subspaces K Θ 2 =H 2 ΘH 2 of the Hardy class H2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels k λ n (z)=(1-Θ(λ n ) ¯Θ(z))/(z-λ ¯ n ) under “small” perturbations of the points λ n . We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces K Θ 2 and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

On étudie les bases et les frames des noyaux reproduisants dans les sous-espaces modèles K Θ 2 =H 2 ΘH 2 de l’espace de Hardy H 2 dans le demi-plan supérieur. On considère le problème de la stabilité d’une base des noyaux reproduisants k λ n (z)=(1-Θ(λ n ) ¯Θ(z))/(z-λ ¯ n ) par rapport aux petites perturbations des pôles λ ¯ n . En utilisant les majorations récentes des derivées dans les espaces K Θ 2 , on obtient les estimations des perturbations admissibles, qui généralisent les théorèmes de W.S. Cohn et E. Fricain.

DOI: 10.5802/aif.2165
Classification: 46E22, 42C15, 30D55, 47B32
Keywords: Inner function, shift-coinvariant subspace, reproducing kernel, Riesz basis, frame, stability, Inner function, shift-coinvariant subspace, reproducing kernel, Riesz basis, frame, stability
Mot clés : fonction intérieure, espace modèle, noyaux reproduisant, base de Riesz, frame, stabilité
Baranov, Anton 1

1 Université Bordeaux 1, Laboratoire d'Analyse et Géométrie, 351 cours de la Libération, 33405 Talence (France), Institutionen för Matematik, Kgl Tekniska Högskolan, 100 44 Stockholm (Suède)
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Baranov, Anton. Stability of the bases and frames reproducing kernels in model spaces. Annales de l'Institut Fourier, Volume 55 (2005) no. 7, pp. 2399-2422. doi : 10.5802/aif.2165. http://archive.numdam.org/articles/10.5802/aif.2165/

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