Discrete Translates in Function Spaces

A. Olevskii, A. Ulanovskii*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


For a wide class of separable Banach function spaces X on ℝ, we construct a Schwartz function φ such that the set of translates {φ(t − λ), λ ∈ Λ} spans X whenever Λ is an exponentially small perturbation of integers. Essentially, the only exception is the space L1(ℝ), which cannot be spanned by a uniformly discrete translates of a single function.

Original languageEnglish
Pages (from-to)251-261
Number of pages11
JournalAnalysis Mathematica
Issue number2
StatePublished - 1 Jun 2018


  • completeness of translates
  • tempered distribution
  • uniformly discrete set


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