Über zufällige Störungen einer Basis aus Exponentialfunktionen im Raum $L_2[-\pi ,\pi ]$

Abstract

We investigate the limit case $|s_n|=1/4$ for the theorem of Paley and Wiener and some later authors on the basis properties of the perturbed system {exp $(i(n+s_n)t):n\in \mathbb{Z}$} in the space $L_2[-\pi ,\pi ]$. We prove that the perturbed system almost sure is no Riesz basis, if {$s_n$} is taken from $[-1/4,1/4{]}^{\mathbb{Z}}$ equipped with natural product measures.