2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68163We characterize, in terms of the Beurling-Malliavin density, the discrete spectra $Λ\subset\R$ for which a generator exists, that is a function $ϕ\in L^1(\R)$ such that its $Λ$-translates $ϕ(x-λ), λ\inΛ$, span $L^1(\R)$. It is shown that these spectra coincide with the uniqueness sets for certain analytic classes. We also present examples of discrete spectra $Λ\subset\R$ which do not admit a single generator while they admit a pair of generators.14 pages, submittedClassical Analysis and ODEsFunctional Analysis42A65;30D60text