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.
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.
Classification : 46E22, 42C15, 30D55, 47B32
Mots 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'institut Fourier}, volume = {55}, number = {7}, year = {2005}, doi = {10.5802/aif.2165}, zbl = {1101.30036}, mrnumber = {2207388}, language = {en}, url = {http://www.numdam.org/item/AIF_2005__55_7_2399_0/} }
Baranov, Anton. Stability of the bases and frames reproducing kernels in model spaces. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2399-2422. doi : 10.5802/aif.2165. http://www.numdam.org/item/AIF_2005__55_7_2399_0/
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