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

Nir Lev; Alexander Olevskii

doi:10.4007/annals.2011.174.1.15

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

Nir Lev, Alexander Olevskii

Weizmann Institute of Science, Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

N. 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 trans- form. He conjectured that a similar characterization should be true for 1 < p < 2. Our main result contradicts this conjecture.

Original language	English
Pages (from-to)	519-541
Number of pages	23
Journal	Annals of Mathematics
Volume	174
Issue number	1
DOIs	https://doi.org/10.4007/annals.2011.174.1.15
State	Published - Jul 2011

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.4007/annals.2011.174.1.15

Cite this

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title = "Wiener's 'closure of translates' problem and Piatetski-Shapiro's uniqueness phenomenon",

abstract = "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.",

author = "Nir Lev and Alexander Olevskii",

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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.

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DO - 10.4007/annals.2011.174.1.15

M3 - مقالة

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JO - Annals of Mathematics

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IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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