2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143431We prove in the vector-valued spaces $L^2(\mathbb{R}_+, X)$ (where $X$ is a finite dimensional Hilbert space) the cyclicity for the semi-group of left translations of some particular functions with support included in a lacunary system of intervals.Spectral Theorytext