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

Details Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon

2009-08-04

arxiv.org/abs/0908.0447v2

Annals of Mathematics 174 (2011), 519-541

Mathematics

Classical Analysis and ODEs

Scientific paper

10.4007/annals.2011.174.1.15

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

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