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Stability of bases and frames of reproducing kernels in model spaces. / Baranov, Anton.

In: Annales de l'Institut Fourier, Vol. 55, No. 7, 01.01.2005.

Research output: Contribution to journal › Article › peer-review

Harvard

Baranov, A 2005, 'Stability of bases and frames of reproducing kernels in model spaces', Annales de l'Institut Fourier, vol. 55, no. 7. https://doi.org/10.5802/aif.2165

APA

Baranov, A. (2005). Stability of bases and frames of reproducing kernels in model spaces. Annales de l'Institut Fourier, 55(7). https://doi.org/10.5802/aif.2165

Vancouver

Baranov A. Stability of bases and frames of reproducing kernels in model spaces. Annales de l'Institut Fourier. 2005 Jan 1;55(7). https://doi.org/10.5802/aif.2165

Author

Baranov, Anton. / Stability of bases and frames of reproducing kernels in model spaces. In: Annales de l'Institut Fourier. 2005 ; Vol. 55, No. 7.

BibTeX

@article{54cf43ce97c748cc94a95ebd8b5e77f6,
title = "Stability of bases and frames of reproducing kernels in model spaces",
abstract = "We study the bases and frames of reproducing kernels in the model subspaces K⊖ 2 = H2 ⊖H2 of the Hardy class H2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels kλn (z) = (1-⊖(λn)⊖(z))/(z - λn) under {"}small{"} perturbations of the points λn. We propose an approach to this problem based on the rerently obtained estimates of derivatives in the spaces K⊖ 2 and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.",
keywords = "Frame, Inner function, Reproducing kernel, Riesz basis, Shift-coinvariant subspace, Stability",
author = "Anton Baranov",
year = "2005",
month = jan,
day = "1",
doi = "10.5802/aif.2165",
language = "English",
volume = "55",
journal = "Annales de l'Institut Fourier",
issn = "0373-0956",
publisher = "Association des Annales de l'Institut Fourier",
number = "7",

}

RIS

TY - JOUR

T1 - Stability of bases and frames of reproducing kernels in model spaces

AU - Baranov, Anton

PY - 2005/1/1

Y1 - 2005/1/1

N2 - We study the bases and frames of reproducing kernels in the model subspaces K⊖ 2 = H2 ⊖H2 of the Hardy class H2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels kλn (z) = (1-⊖(λn)⊖(z))/(z - λn) under "small" perturbations of the points λn. We propose an approach to this problem based on the rerently obtained estimates of derivatives in the spaces K⊖ 2 and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

AB - We study the bases and frames of reproducing kernels in the model subspaces K⊖ 2 = H2 ⊖H2 of the Hardy class H2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels kλn (z) = (1-⊖(λn)⊖(z))/(z - λn) under "small" perturbations of the points λn. We propose an approach to this problem based on the rerently obtained estimates of derivatives in the spaces K⊖ 2 and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

KW - Frame

KW - Inner function

KW - Reproducing kernel

KW - Riesz basis

KW - Shift-coinvariant subspace

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=33751505305&partnerID=8YFLogxK

U2 - 10.5802/aif.2165

DO - 10.5802/aif.2165

M3 - Article

AN - SCOPUS:33751505305

VL - 55

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

SN - 0373-0956

IS - 7

ER -

ID: 32721663