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Piatetski-Shapiro phenomenon in the uniqueness problem. (English. Abridged French version) Zbl 1063.43006

Summary: We extend the phenomenon discovered by I. I. Piatetski-Shapiro [Moskov. Univ. Uchen. Zapiski Mat. 165, No. 7, 79–97 (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.

MSC:

43A45 Spectral synthesis on groups, semigroups, etc.
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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