Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$

Chistyakov, Gennadii; Lyubarskii, Yura

Random perturbations of exponential Riesz bases in

L^{2} (- π, π)

Chistyakov, Gennadii ; Lyubarskii, Yura

Annales de l'Institut Fourier, Tome 47 (1997), p. 201-255 / Harvested from Numdam

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Abstract

Soient ${λ_{n}} \subset ℝ$ une suite donnée telle que le système exponentiel ${\exp (i λ_{n} x)}$ forme une base de Riesz dans $L^{2} (- π, π)$ et ${ξ_{n}}$ une suite de variables aléatoires réelles indépendantes. On étudie les propriétés du système ${\exp (i (λ_{n} + ξ_{n}) x)}$ ainsi que des problèmes reliés aux estimations des fonctions entières ayant des zéros aléatoires, et des problèmes de reconstitution de signaux avec un spectre de largeur $2 π$ à l’aide de valeurs de ces signaux dans des points aléatoires ${λ_{n} + ξ_{n}}$ .

Let a sequence ${λ_{n}} \subset ℝ$ 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 ${λ_{n} + ξ_{n}}$ .

Publié le : 1997-01-01

MR 98c:42028 | Zbl 0860.42023

DOI : https://doi.org/10.5802/aif.1565

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     author = {Chistyakov, Gennadii and Lyubarskii, Yura},
     title = {Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$},
     journal = {Annales de l'Institut Fourier},
     volume = {47},
     year = {1997},
     pages = {201-255},
     doi = {10.5802/aif.1565},
     mrnumber = {98c:42028},
     zbl = {0860.42023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1997__47_1_201_0}
}

Chistyakov, Gennadii; Lyubarskii, Yura. Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$. Annales de l'Institut Fourier, Tome 47 (1997) pp. 201-255. doi : 10.5802/aif.1565. http://gdmltest.u-ga.fr/item/AIF_1997__47_1_201_0/

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