Multi-tiling and Riesz bases

Sigrid Grepstad; Nir Lev

doi:10.1016/j.aim.2013.10.019

Multi-tiling and Riesz bases

Sigrid Grepstad, Nir Lev

Department of Mathematics

Bar-Ilan University

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

Abstract

Let S be a bounded, Riemann measurable set in Rd, and Λ be a lattice. By a theorem of Fuglede, if S tiles Rd with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles Rd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals.

Original language	English
Pages (from-to)	1-6
Number of pages	6
Journal	Advances in Mathematics
Volume	252
DOIs	https://doi.org/10.1016/j.aim.2013.10.019
State	Published - 15 Feb 2014

Keywords

Quasicrystals
Riesz bases
Tiling

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2013.10.019

Cite this

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title = "Multi-tiling and Riesz bases",

abstract = "Let S be a bounded, Riemann measurable set in Rd, and Λ be a lattice. By a theorem of Fuglede, if S tiles Rd with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles Rd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals.",

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AU - Lev, Nir

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N2 - Let S be a bounded, Riemann measurable set in Rd, and Λ be a lattice. By a theorem of Fuglede, if S tiles Rd with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles Rd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals.

AB - Let S be a bounded, Riemann measurable set in Rd, and Λ be a lattice. By a theorem of Fuglede, if S tiles Rd with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles Rd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals.

KW - Quasicrystals

KW - Riesz bases

KW - Tiling

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DO - 10.1016/j.aim.2013.10.019

M3 - مقالة

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VL - 252

SP - 1

EP - 6

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Multi-tiling and Riesz bases

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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