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 language | English |
|---|---|
| Pages (from-to) | 879-898 |
| Number of pages | 20 |
| Journal | Journal of Fourier Analysis and Applications |
| Volume | 17 |
| Issue number | 5 |
| State | Published - Oct 2011 |
| Externally published | Yes |
Keywords
- Bounded mean oscillation
- Discrepancy
- Quasicrystals
- Riesz bases