This is an announcement for the paper "Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon" by Nir Lev and Alexander Olevskii.

Abstract: Wiener characterized the cyclic vectors (with respect to translations) in $l^p(Z)$ and $L^p(R)$, $p=1,2$, 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.

Archive classification: math.CA math.FA

Mathematics Subject Classification: 42A63 (Primary) 43A45, 47A16 (Secondary)

Citation: Annals of Mathematics 174 (2011), 519-541

Submitted from: levnir@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0908.0447

or

http://arXiv.org/abs/0908.0447