Resumen de Completeness in L^1(R) of discrete translates

Joaquim Bruna i Floris , Alexander Olevskii, Alexander Ulanovskii

• We characterize, in terms of the Beurling-Malliavin density, the discrete spectra ? Ì R for which a generator exists, that is a function f Î L1(R) such that its ? translates f(x - ?), ? Î ?, span L1(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra ? Î R which do not admit a single generator while they admit a pair of generators.