We study the bases and frames of reproducing kernels in the model subspaces of the Hardy class in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels under “small” perturbations of the points . We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces 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 de l’espace de Hardy dans le demi-plan supérieur. On considère le problème de la stabilité d’une base des noyaux reproduisants par rapport aux petites perturbations des pôles . En utilisant les majorations récentes des derivées dans les espaces , on obtient les estimations des perturbations admissibles, qui généralisent les théorèmes de W.S. Cohn et E. Fricain.
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
@article{AIF_2005__55_7_2399_0, author = {Baranov, Anton}, title = {Stability of the bases and frames reproducing kernels in model spaces}, journal = {Annales de l'Institut Fourier}, pages = {2399--2422}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {7}, year = {2005}, doi = {10.5802/aif.2165}, mrnumber = {2207388}, zbl = {1101.30036}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2165/} }
TY - JOUR AU - Baranov, Anton TI - Stability of the bases and frames reproducing kernels in model spaces JO - Annales de l'Institut Fourier PY - 2005 SP - 2399 EP - 2422 VL - 55 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2165/ DO - 10.5802/aif.2165 LA - en ID - AIF_2005__55_7_2399_0 ER -
%0 Journal Article %A Baranov, Anton %T Stability of the bases and frames reproducing kernels in model spaces %J Annales de l'Institut Fourier %D 2005 %P 2399-2422 %V 55 %N 7 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2165/ %R 10.5802/aif.2165 %G en %F AIF_2005__55_7_2399_0
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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