Completeness in L1 (ℝ) of discrete translates

Joaquim Bruna, Alexander Olevskii, Alexander Ulanovskii

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-16
JournalRevista Matematica Iberoamericana
Volume22
Issue number1
Publication statusPublished - 10 Oct 2006

Keywords

  • Bernstein classes
  • Beurling-Malliavin density
  • Discrete translates
  • Generator
  • Uniqueness sets

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