no. 11
Mathematical Analysis
Piatetski-Shapiro phenomenon in the uniqueness problem
Presented by: Jean-Pierre Kahane
Lev, Nir1; Olevskii, Alexander1
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

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

Nous étendons aux espaces lq 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 lq, mais qui ne porte pas de mesure ayant cette propriété.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.04.031

Lev, Nir 1; Olevskii, Alexander 1

1 School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel 
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Lev, Nir; Olevskii, Alexander. 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

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