Discrete Translates in Function Spaces

A. Olevskii, A. Ulanovskii

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)251-261
Number of pages11
JournalAnalysis Mathematica
Volume44
Issue number2
DOIs
StatePublished - 1 Jun 2018

Keywords

  • completeness of translates
  • tempered distribution
  • uniformly discrete set

Fingerprint

Dive into the research topics of 'Discrete Translates in Function Spaces'. Together they form a unique fingerprint.

Cite this