Wiener’s `closure of translates’ problem and Piatetski-Shapiro’s  uniqueness phenomenon

Nir Lev; Alexander Olevskii

doi:http://doi.org/10.4007/annals.2011.174.1.15

Abstract

N. Wiener characterized the cyclic vectors (with respect to translations) in $\ell^p(\mathbb{Z})$ and $L^p(\mathbb{R})$, $p=1,2$, in terms of the zero set of the Fourier transform. He conjectured that a similar characterization should be true for $1 < p < 2$. Our main result contradicts this conjecture.

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Wiener’s `closure of translates’ problem and Piatetski-Shapiro’s uniqueness phenomenon

Abstract

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