## Abstract

Given 1 < p < 2 we construct two continuous functions f and g on the circle, with the following properties:. (i) They have the same set of zeros;. (ii) The Fourier transforms over(f, ̂) and over(g, ̂) both belong to ℓ^{p} (Z);. (iii) The translates of over(g, ̂) span the whole ℓ^{p}, but those of over(f, ̂) do not. A similar result is true for L^{p} (R). This should be contrasted with the Wiener theorems related to p = 1, 2. To cite this article: N. Lev, A. Olevskii, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original language | English |
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Pages (from-to) | 645-648 |

Number of pages | 4 |

Journal | Comptes Rendus Mathematique |

Volume | 346 |

Issue number | 11-12 |

DOIs | |

State | Published - Jun 2008 |

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