Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

Gady Kozma; Nir Lev

doi:https://doi.org/10.1007/s00041-011-9178-1

Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

Gady Kozma, Nir Lev

Department of Mathematics

Weizmann Institute of Science

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

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

Keywords

Bounded mean oscillation
Discrepancy
Quasicrystals
Riesz bases

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
General Mathematics

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https://doi.org/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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AU - Lev, Nir

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N2 - 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.

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.

KW - Bounded mean oscillation

KW - Discrepancy

KW - Quasicrystals

KW - Riesz bases

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M3 - مقالة

SN - 1069-5869

VL - 17

SP - 879

EP - 898

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 5

ER -

Exponential Riesz Bases, Discrepancy of Irrational Rotations and BMO

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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