Piatetski-Shapiro phenomenon in the uniqueness problem

Nir Lev; Alexander Olevskii

doi:10.1016/j.crma.2005.04.031

Mathematical Analysis

Piatetski-Shapiro phenomenon in the uniqueness problem

Presented by: Jean-Pierre Kahane

Nir Lev ¹; Alexander Olevskii ¹

¹ School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel

Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 793-798.

Abstract
Résumé

We extend the phenomenon discovered by Piatetski-Shapiro (1954) to $l^{q}$ spaces. To be precise, for any $q > 2$ we construct a compact K on the circle, which supports a distribution S with Fourier transform $\hat{S} \in l^{q}$ , but does not support such a measure.

Nous étendons aux espaces $l^{q}$ le phénomène découvert par Piatetski-Shapiro en 1954 : pour tout $q > 2$ nous construisons un compact K sur le cercle, qui porte une distribution dont la transformée de Fourier appartient à $l^{q}$ , mais qui ne porte pas de mesure ayant cette propriété.

Received: 2005-04-19
Accepted: 2005-04-27
Published online: 2005-05-23

DOI: 10.1016/j.crma.2005.04.031

Author's affiliations:

Nir Lev ¹; Alexander Olevskii ¹

¹ School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel

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     title = {Piatetski-Shapiro phenomenon in the uniqueness problem},
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     pages = {793--798},
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     year = {2005},
     doi = {10.1016/j.crma.2005.04.031},
     language = {en},
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Nir Lev; Alexander Olevskii. Piatetski-Shapiro phenomenon in the uniqueness problem. Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 793-798. doi : 10.1016/j.crma.2005.04.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.031/

References
Cited by

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