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

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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.

Original languageEnglish
Pages (from-to)519-541
Number of pages23
JournalAnnals of Mathematics
Volume174
Issue number1
DOIs
StatePublished - Jul 2011

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