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

¹ School of Mathematics, Tel Aviv University, 69978 Ramat Aviv, Israel.
² Stavanger 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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     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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.142/

References
Cited by

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[2] Pavel Kurasov; Peter C. Sarnak Stable polynomials and crystalline measures, J. Math. Phys., Volume 61 (2020) no. 8, 083501, 13 pages | DOI | MR | Zbl

[3] Nir Lev; Alexander Olevskii Quasicrystals with discrete support and spectrum, Rev. Mat. Iberoam., Volume 32 (2016) no. 4, pp. 1341-1352 | MR | Zbl

[4] Boris Ya. Levin Lectures on Entire Fuctions, Translations of Mathematical Monographs, 150, American Mathematical Society, 1996 | Zbl

[5] Yves F. Meyer Quasicrystals, diophantine approximation and algebraic numbers, Beyond quasicrystals. Papers of the winter school, Les Houches, France, March 7-18, 1994, Springer, 1995, pp. 3-16 | DOI | Zbl

[6] Yves F. Meyer Measures with locally finite support and spectrum, Proc. Natl. Acad. Sci. USA, Volume 113 (2016) no. 12, pp. 3152-3158 | DOI | MR | Zbl

[7] Yves F. Meyer Measures with locally finite support and spectrum, Rev. Mat. Iberoam., Volume 33 (2017) no. 3, pp. 1025-1036 | DOI | MR | Zbl

[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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