Exponential Riesz bases, discrepancy of irrational rotations and BMO

Details Exponential Riesz bases, discrepancy of irrational rotations and BMO Exponential Riesz bases, discrepancy of irrational rotations and BMO

2010-09-11

arxiv.org/abs/1009.2188v2

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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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