Universal sampling, quasicrystals and bounded remainder sets

Sigrid Grepstad; Nir Lev

doi:10.1016/j.crma.2014.05.006

Universal sampling, quasicrystals and bounded remainder sets

Sigrid Grepstad, Nir Lev

Department of Mathematics

Bar-Ilan University

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

Abstract

We examine the result due to Matei and Meyer that simple quasicrystals are universal sampling sets, in the critical case when the density of the sampling set is equal to the measure of the spectrum. We show that in this case, an arithmetical condition on the quasicrystal determines whether it is a universal set of "stable and non-redundant" sampling.

Original language	English
Pages (from-to)	633-638
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	352
Issue number	7-8
DOIs	https://doi.org/10.1016/j.crma.2014.05.006
State	Published - Jul 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2014.05.006

Cite this

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title = "Universal sampling, quasicrystals and bounded remainder sets",

abstract = "We examine the result due to Matei and Meyer that simple quasicrystals are universal sampling sets, in the critical case when the density of the sampling set is equal to the measure of the spectrum. We show that in this case, an arithmetical condition on the quasicrystal determines whether it is a universal set of {"}stable and non-redundant{"} sampling.",

author = "Sigrid Grepstad and Nir Lev",

note = "Funding Information: Research partially supported by the Israel Science Foundation Grant No. 225/13 .",

year = "2014",

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doi = "10.1016/j.crma.2014.05.006",

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T1 - Universal sampling, quasicrystals and bounded remainder sets

AU - Grepstad, Sigrid

AU - Lev, Nir

N1 - Funding Information: Research partially supported by the Israel Science Foundation Grant No. 225/13 .

PY - 2014/7

Y1 - 2014/7

N2 - We examine the result due to Matei and Meyer that simple quasicrystals are universal sampling sets, in the critical case when the density of the sampling set is equal to the measure of the spectrum. We show that in this case, an arithmetical condition on the quasicrystal determines whether it is a universal set of "stable and non-redundant" sampling.

AB - We examine the result due to Matei and Meyer that simple quasicrystals are universal sampling sets, in the critical case when the density of the sampling set is equal to the measure of the spectrum. We show that in this case, an arithmetical condition on the quasicrystal determines whether it is a universal set of "stable and non-redundant" sampling.

UR - http://www.scopus.com/inward/record.url?scp=84905036692&partnerID=8YFLogxK

U2 - 10.1016/j.crma.2014.05.006

DO - 10.1016/j.crma.2014.05.006

M3 - مقالة

SN - 1631-073X

VL - 352

SP - 633

EP - 638

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 7-8

ER -

Universal sampling, quasicrystals and bounded remainder sets

Abstract

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