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 -