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.
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Communicated by Yurii Lyubarskii.
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Kozma, G., Lev, N. Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO. J Fourier Anal Appl 17, 879–898 (2011). https://doi.org/10.1007/s00041-011-9178-1
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DOI: https://doi.org/10.1007/s00041-011-9178-1