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Random perturbations of exponential Riesz bases in \(L^ 2(-\pi,\pi)\). (English) Zbl 0860.42023
Summary: Let a sequence \(\{\lambda_n\}\subset {\mathbb{R}}\) be given such that the exponential system \(\{\text{exp} (i \lambda_n x)\}\) forms a Riesz basis in \(L^2(-\pi,\pi)\) and \(\{\xi_n\}\) be a sequence of independent real-valued random variables. We study the properties of the system \(\{\text{exp}(i (\lambda_n+\xi_n) x)\}\) 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 \(\{\lambda_n+\xi_n\}\).

MSC:
42C15 General harmonic expansions, frames
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
60H25 Random operators and equations (aspects of stochastic analysis)
30D10 Representations of entire functions of one complex variable by series and integrals
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