On translation and affine systems spanning L1(ℝ)

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Abstract

We show that the discrete translation parameter sets ∧ ⊂ ℝ for which some φ ∈ L1 ℝ exists such that the translates φ(x - λ), λ ∈, ∧ span L1ℝ are exactly the uniqueness sets for certain quasianalytic classes, and give explicit constructions of such generators φ. We also consider a similar situation for affine systems of the type φ(μx - λ), μ ∈Γ, λ ∈. ∧ © Birkhäuser Boston. All rights reserved.
Original languageEnglish
Pages (from-to)71-82
JournalJournal of Fourier Analysis and Applications
Volume12
DOIs
Publication statusPublished - 1 Feb 2006

Keywords

  • Densities
  • Quasianalytic classes
  • Spanning functions
  • Translates
  • Uniqueness sets

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