2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60610We prove several results related to the theorem of Logvinenko and Sereda on determining sets for functions with Fourier transforms supported in an interval. We obtain a polynomial instead of exponential bound in this theorem, and we extend it to the case of functions with Fourier transforms supported in the union of a bounded number of intervals. The same results hold in all dimensions.to appear in PAMSClassical Analysis and ODEsAnalysis of PDEs42text