Geodesic
Wiener’s `closure of translates’ problem and Piatetski-Shapiro’s uniqueness phenomenon
Nir Lev1 ; Alexander Olevskii2
1 Faculty of Mathematics and Computer Science <br/> The Weizmann Institute of Science<br/> Rehovot 76100<br/> Israel
2 School of Mathematical Sciences<br/> Tel Aviv University<br/> Ramat Aviv<br/> Tel Aviv, 69978<br/>Israel
Annals of mathematics, Tome 174 (2011) no. 1, pp. 519-541.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2011.174.1.15

Nir Lev 1 ; Alexander Olevskii 2

1 Faculty of Mathematics and Computer Science <br/> The Weizmann Institute of Science<br/> Rehovot 76100<br/> Israel
2 School of Mathematical Sciences<br/> Tel Aviv University<br/> Ramat Aviv<br/> Tel Aviv, 69978<br/>Israel 
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Nir Lev; Alexander Olevskii. Wiener’s `closure of translates’ problem and Piatetski-Shapiro’s  uniqueness phenomenon. Annals of mathematics, Tome 174 (2011) no. 1, pp. 519-541. doi : 10.4007/annals.2011.174.1.15. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.1.15/

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