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