Sets of p-restriction and p-spectral synthesis

Abstract

In this paper we investigate the restriction problem. More precisely, we give sufficient conditions for the failure of a set E in ℝn to have the p-restriction property. We also extend the concept of spectral synthesis to Lp(ℝn) 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 ℝn when n ⩾ 3.

Keywords

• p-spectral synthesis
• restriction problem
• set of p-restriction
• span of translates
• 42b10
• 43a15