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Analysis Mathematica

, Volume 44, Issue 2, pp 251–261 | Cite as

Discrete Translates in Function Spaces

  • A. Olevskii
  • A. Ulanovskii
Article
  • 102 Downloads

Abstract

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.

Key words and phrases

completeness of translates uniformly discrete set tempered distribution 

Mathematics Subject Classification

primary 42A65 secondary 46F99 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.School of MathematicsTel Aviv UniversityRamat AvivIsrael
  2. 2.Stavanger UniversityStavangerNorway

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