Stability of the bases and frames reproducing kernels in model spaces

Anton Baranov[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)

Annales de l'institut Fourier (2005)

  • Volume: 55, Issue: 7, page 2399-2422
  • ISSN: 0373-0956

Abstract

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We study the bases and frames of reproducing kernels in the model subspaces K Θ 2 = H 2 ⊖ Θ H 2 of the Hardy class H 2 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.

How to cite

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Baranov, Anton. "Stability of the bases and frames reproducing kernels in model spaces." Annales de l'institut Fourier 55.7 (2005): 2399-2422. <http://eudml.org/doc/116258>.

@article{Baranov2005,
abstract = {We study the bases and frames of reproducing kernels in the model subspaces $K^2_\{\Theta \}=H^2\ominus \Theta H^2$ of the Hardy class $H2$ in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels $k_\{\lambda _n\}(z)= (1-\overline\{\Theta (\lambda _n)\}\Theta (z))/(z-\overline\{\lambda \}_n)$ under “small” perturbations of the points $\lambda _n$. We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces $\{K^2_\{\Theta \}\}$ and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.},
affiliation = {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)},
author = {Baranov, Anton},
journal = {Annales de l'institut Fourier},
keywords = {Inner function; shift-coinvariant subspace; reproducing kernel; Riesz basis; frame; stability; inner function},
language = {eng},
number = {7},
pages = {2399-2422},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stability of the bases and frames reproducing kernels in model spaces},
url = {http://eudml.org/doc/116258},
volume = {55},
year = {2005},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 7
SP - 2399
EP - 2422
AB - We study the bases and frames of reproducing kernels in the model subspaces $K^2_{\Theta }=H^2\ominus \Theta H^2$ of the Hardy class $H2$ in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels $k_{\lambda _n}(z)= (1-\overline{\Theta (\lambda _n)}\Theta (z))/(z-\overline{\lambda }_n)$ under “small” perturbations of the points $\lambda _n$. We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces ${K^2_{\Theta }}$ and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.
LA - eng
KW - Inner function; shift-coinvariant subspace; reproducing kernel; Riesz basis; frame; stability; inner function
UR - http://eudml.org/doc/116258
ER -

References

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