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Zeitschrift für Analysis und ihre Anwendungen


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Volume 1, Issue 4, 1982, pp. 31–36
DOI: 10.4171/ZAA/26

Published online: 1982-08-31

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

Klaus-Detlef Kürsten[1]

(1) Universität Leipzig, Germany

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.

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Kürsten Klaus-Detlef: Über zufällige Störungen einer Basis aus Exponentialfunktionen im Raum $L_2 [-\pi, \pi]$. Z. Anal. Anwend. 1 (1982), 31-36. doi: 10.4171/ZAA/26