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 .
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 .
@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}, 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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