Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-16 |
| Journal | Revista Matematica Iberoamericana |
| Volume | 22 |
| Issue number | 1 |
| Publication status | Published - 10 Oct 2006 |
Keywords
- Bernstein classes
- Beurling-Malliavin density
- Discrete translates
- Generator
- Uniqueness sets