Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

Gady Kozma, Nir Lev

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We study the basis property of systems of exponentials with frequencies belonging to 'simple quasicrystals'. We show that a diophantine condition is necessary and sufficient for such a system to be a Riesz basis in L2 on a finite union of intervals. For the proof we extend to BMO a theorem of Kesten about the discrepancy of irrational rotations of the circle.

Original languageEnglish
Pages (from-to)879-898
Number of pages20
JournalJournal of Fourier Analysis and Applications
Volume17
Issue number5
DOIs
StatePublished - Oct 2011
Externally publishedYes

Keywords

  • Bounded mean oscillation
  • Discrepancy
  • Quasicrystals
  • Riesz bases

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