Let a sequence be given such that the exponential system forms a Riesz basis in and be a sequence of independent real-valued random variables. We study the properties of the system as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth via their samples at the random points .
Soient une suite donnée telle que le système exponentiel forme une base de Riesz dans et une suite de variables aléatoires réelles indépendantes. On étudie les propriétés du système 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 à l’aide de valeurs de ces signaux dans des points aléatoires .
@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}, pages = {201--255}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {47}, number = {1}, year = {1997}, doi = {10.5802/aif.1565}, zbl = {0860.42023}, mrnumber = {98c:42028}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1565/} }
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 SP - 201 EP - 255 VL - 47 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1565/ DO - 10.5802/aif.1565 LA - en ID - AIF_1997__47_1_201_0 ER -
%0 Journal Article %A Chistyakov, Gennadii %A Lyubarskii, Yura %T Random perturbations of exponential Riesz bases in $L^2(-\pi ,\pi )$ %J Annales de l'Institut Fourier %D 1997 %P 201-255 %V 47 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1565/ %R 10.5802/aif.1565 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.1565/
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