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Exponential Riesz bases, discrepancy of irrational rotations and BMO (1009.2188v2)
Published 11 Sep 2010 in math.CA
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.