Discrete uniqueness sets for functions with spectral gaps
Abstract
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 nonuniqueness property: every discrete function c(λ)\in l^2(Λ) can be interpolated by an analytic L^2function with spectrum in S.
Bibliography: 9 titles.
 Publication:

Sbornik: Mathematics
 Pub Date:
 June 2017
 DOI:
 10.1070/SM8837
 arXiv:
 arXiv:1609.04571
 Bibcode:
 2017SbMat.208..863O
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 42A64;
 42A99
 EPrint:
 doi:10.1070/SM8837