TY - JOUR
T1 - Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon
AU - Lev, Nir
AU - Olevskii, Alexander
PY - 2011/7
Y1 - 2011/7
N2 - N. Wiener characterized the cyclic vectors (with respect to translations) in lp(Z) and Lp(R), p = 1, 2, in terms of the zero set of the Fourier trans- form. He conjectured that a similar characterization should be true for 1 < p < 2. Our main result contradicts this conjecture.
AB - N. Wiener characterized the cyclic vectors (with respect to translations) in lp(Z) and Lp(R), p = 1, 2, in terms of the zero set of the Fourier trans- form. He conjectured that a similar characterization should be true for 1 < p < 2. Our main result contradicts this conjecture.
UR - http://www.scopus.com/inward/record.url?scp=79959947635&partnerID=8YFLogxK
U2 - 10.4007/annals.2011.174.1.15
DO - 10.4007/annals.2011.174.1.15
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SN - 0003-486X
VL - 174
SP - 519
EP - 541
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 1
ER -