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 Ŝ ∈ lq, but does not support such a measure.
|Translated title of the contribution||Piatetski-Shapiro phenomenon in the uniqueness problem|
|Number of pages||6|
|Journal||Comptes Rendus Mathematique|
|State||Published - 1 Jun 2005|