In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set E in ℝ n to have the p -restriction property. We also extend the concept of spectral synthesis to L p (ℝ n ) for sets of p -restriction when p 1. We use our results to show that there are p -values for which the unit sphere is a set of p -spectral synthesis in ℝ n when n ⩾ 3.
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