Let a sequence $\left\{{\lambda }_n\right\}\subset ℝ$ be given such that the exponential system $\left\{\exp \right(i{\lambda }_{n}x\left)\right\}$ forms a Riesz basis in $L^2(-\pi ,\pi )$ and $\left\{{\xi }_n\right\}$ be a sequence of independent real-valued random variables. We study the properties of the system $\{exp(i({\lambda }_n+{\xi }_n)x\left)\right\}$ 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 $\{{\lambda }_n+{\xi }_n\}$.

Dans le chapitre I on indique la croissance de $\omega$ et de la fonction convexe $C$ pour que de $log\left|F\right(z\left)\right|\le \pi \left|y\right|-\omega \left(\right|y\left|\right)$$(y=\mathrm{Im}z)...$