Random perturbations of exponential Riesz bases in L 2 (-π,π)
Annales de l'Institut Fourier, Volume 47 (1997) no. 1, p. 201-255

Let a sequence {λ n } be given such that the exponential system { exp (iλ 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 2π via their samples at the random points {λ n +ξ n }.

Soient {λ n } une suite donnée telle que le système exponentiel { exp (iλ 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 2π à l’aide de valeurs de ces signaux dans des points aléatoires {λ n +ξ n }.

@article{AIF_1997__47_1_201_0,
     author = {Chistyakov, Gennadii and Lyubarskii, Yura},
     title = {Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {47},
     number = {1},
     year = {1997},
     pages = {201-255},
     doi = {10.5802/aif.1565},
     zbl = {0860.42023},
     mrnumber = {98c:42028},
     language = {en},
     url = {http://www.numdam.org/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, Volume 47 (1997) no. 1, pp. 201-255. doi : 10.5802/aif.1565. http://www.numdam.org/item/AIF_1997__47_1_201_0/

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