Fourier Quasicrystals with Unit Masses

Alexander Olevskii; Alexander Ulanovskii

doi:10.5802/crmath.142

Harmonic Analysis

Fourier Quasicrystals with Unit Masses

Alexander Olevskii ¹; Alexander Ulanovskii ²

¹School of Mathematics, Tel Aviv University, 69978 Ramat Aviv, Israel.
²Stavanger University, 4036 Stavanger, Norway.

Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1207-1211

Abstract

The sum of $δ$ -measures sitting at the points of a discrete set $Λ \subset ℝ$ forms a Fourier quasicrystal if and only if $Λ$ is the zero set of an exponential polynomial with imaginary frequencies.

Received: 2020-10-19
Accepted: 2020-10-30
Published online: 2021-01-25

DOI: 10.5802/crmath.142

Author's affiliations:

Alexander Olevskii ¹ ; Alexander Ulanovskii ²

¹ School of Mathematics, Tel Aviv University, 69978 Ramat Aviv, Israel.
² Stavanger University, 4036 Stavanger, Norway.

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Alexander Olevskii and Alexander Ulanovskii},
     title = {Fourier {Quasicrystals} with {Unit} {Masses}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1207--1211},
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     number = {11-12},
     doi = {10.5802/crmath.142},
     language = {en},
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Alexander Olevskii; Alexander Ulanovskii. Fourier Quasicrystals with Unit Masses. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1207-1211. doi: 10.5802/crmath.142

References
Cited by

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[8] Yves F. Meyer Curved model sets and crystalline measures (2020) (to be published in Applied and Numerical Harmonic Analysis, Springer)

[9] Alexander Olevskii; Alexander Ulanovskii Fourier quasicrystals with unit masses (2020) (https://arxiv.org/abs/2009.12810)

[10] Alexander Olevskii; Alexander Ulanovskii A Simple Crystalline Measure (2020) (https://arxiv.org/abs/2006.12037)

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