Discrete uniqueness sets for functions with spectral gaps

A. Olevskii, A. Ulanovskii

Research output: Contribution to journalArticlepeer-review


It is well known that entire functions whose spectrum belongs to a fixed bounded set S admit real uniformly discrete uniqueness sets. We show that the same is true for a much wider range of spaces of continuous functions. In particular, Sobolev spaces have this property whenever S is a set of infinite measure having 'periodic gaps'. The periodicity condition is crucial. For sets S with randomly distributed gaps, we show that uniformly discrete sets Λ satisfy a strong non-uniqueness property: every discrete function c(λ) G l2 (Λ) can be interpolated by an analytic L2-function with spectrum in S.

Original languageEnglish
Pages (from-to)863-877
Number of pages15
JournalSbornik Mathematics
Issue number6
StatePublished - 2017


  • Discrete uniqueness set
  • Fourier transform
  • Sobolev space
  • Spectral gap


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