We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ ℝ for which a generator exists, that is a function φ ∈ L1(ℝ) such that its Λ-translates φ(x - λ), λ ∈ Λ, span L1(ℝ). It is shown that these spectra coincide with the uniqueness sets for certain analytic classes. We also present examples of discrete spectra Λ ⊂ ℝ which do not admit a single generator while they admit a pair of generators.
|Journal||Revista Matematica Iberoamericana|
|Publication status||Published - 10 Oct 2006|
- Bernstein classes
- Beurling-Malliavin density
- Discrete translates
- Uniqueness sets