English

Exponential Riesz bases, discrepancy of irrational rotations and BMO

Classical Analysis and ODEs 2011-03-15 v2

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 L^2 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.

Cite

@article{arxiv.1009.2188,
  title  = {Exponential Riesz bases, discrepancy of irrational rotations and BMO},
  author = {Gady Kozma and Nir Lev},
  journal= {arXiv preprint arXiv:1009.2188},
  year   = {2011}
}

Comments

16 pages, to appear in J. Fourier Analysis and Applications