Approximation of discrete functions and size of spectrum

A. Olevski̧*, A. Ulanovski̧

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let Λ ⊂ R be a uniformly discrete sequence and S ⊂ R a compact set. It is proved that if there exists a bounded sequence of functions in the Paley-Wiener space PWS that approximates δ-functions on Λ with l2-error d, then the measure ofS cannot be less than 2π(1 - d2)D+(Λ). This estimate is sharp for every d. A similar estimate holds true when the normsof the approximating functions have a moderate growth; the corresponding sharp growth restriction is found.

Original languageEnglish
Pages (from-to)1015-1025
Number of pages11
JournalSt. Petersburg Mathematical Journal
Issue number6
StatePublished - 2010


  • Approximation of discrete functions
  • Bernstein space
  • Paley-Wiener space
  • Set of interpolation


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