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.
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