Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

Gady Kozma; Nir Lev

doi:10.1007/s00041-011-9178-1

Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

Gady Kozma
, Nir Lev

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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
DOIs	https://doi.org/10.1007/s00041-011-9178-1
State	Published - Oct 2011
Externally published	Yes

Keywords

Bounded mean oscillation
Discrepancy
Quasicrystals
Riesz bases

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10.1007/s00041-011-9178-1

Cite this

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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.",

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AB - 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.

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KW - Discrepancy

KW - Quasicrystals

KW - Riesz bases

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Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

Abstract

Keywords

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