We characterize, in terms of the Beurling-Malliavin density, the discrete spectra for which a generator exists, that is a function such that its -translates , span . It is shown that these spectra coincide with the uniqueness sets for certain analytic classes. We also present examples of discrete spectra which do not admit a single generator while they admit a pair of generators.
Cite this article
Joaquim Bruna, Alexander Olevskiǐ, Alexander Ulanovskii, Completeness in of discrete translates. Rev. Mat. Iberoam. 22 (2006), no. 1, pp. 1–16DOI 10.4171/RMI/447