Random perturbations of exponential Riesz bases in L 2 ( - π , π )

Gennadii Chistyakov; Yura Lyubarskii

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 1, page 201-255
  • ISSN: 0373-0956

Abstract

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Let a sequence { λ n } ⊂ ℝ be given such that the exponential system { exp ( i λ n x ) } forms a Riesz basis in L 2 ( - π , π ) and { ξ n } be a sequence of independent real-valued random variables. We study the properties of the system { exp ( i ( λ n + ξ n ) x ) } as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth 2 π via their samples at the random points { λ n + ξ n } .

How to cite

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Chistyakov, Gennadii, and Lyubarskii, Yura. "Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$." Annales de l'institut Fourier 47.1 (1997): 201-255. <http://eudml.org/doc/75227>.

@article{Chistyakov1997,
abstract = {Let a sequence $\lbrace \lambda _n\rbrace \subset \{\Bbb R\}$ be given such that the exponential system $\lbrace \{\rm exp\}\,(i \lambda _n x)\rbrace $ forms a Riesz basis in $L^2(-\pi ,\pi )$ and $\lbrace \xi _n\rbrace $ be a sequence of independent real-valued random variables. We study the properties of the system $\lbrace \{\rm \exp \}(i (\lambda _n+\xi _n) x)\rbrace $ as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth $2\pi $ via their samples at the random points $\lbrace \lambda _n+\xi _n\rbrace $.},
author = {Chistyakov, Gennadii, Lyubarskii, Yura},
journal = {Annales de l'institut Fourier},
keywords = {exponential system; Riesz basis; reconstruction},
language = {eng},
number = {1},
pages = {201-255},
publisher = {Association des Annales de l'Institut Fourier},
title = {Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$},
url = {http://eudml.org/doc/75227},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Chistyakov, Gennadii
AU - Lyubarskii, Yura
TI - Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 1
SP - 201
EP - 255
AB - Let a sequence $\lbrace \lambda _n\rbrace \subset {\Bbb R}$ be given such that the exponential system $\lbrace {\rm exp}\,(i \lambda _n x)\rbrace $ forms a Riesz basis in $L^2(-\pi ,\pi )$ and $\lbrace \xi _n\rbrace $ be a sequence of independent real-valued random variables. We study the properties of the system $\lbrace {\rm \exp }(i (\lambda _n+\xi _n) x)\rbrace $ as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth $2\pi $ via their samples at the random points $\lbrace \lambda _n+\xi _n\rbrace $.
LA - eng
KW - exponential system; Riesz basis; reconstruction
UR - http://eudml.org/doc/75227
ER -

References

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