Fourier quasicrystals and discreteness of the diffraction spectrum

Nir Lev; Alexander Olevskii

doi:10.1016/j.aim.2017.05.015

Fourier quasicrystals and discreteness of the diffraction spectrum

Nir Lev, Alexander Olevskii

Department of Mathematics

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

14 Scopus citations

Abstract

We prove that a positive-definite measure in Rⁿ with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent results where we proved this under the assumption that also the spectrum is uniformly discrete. As an application we obtain that Hof's quasicrystals with uniformly discrete diffraction spectra must have a periodic diffraction structure.

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Advances in Mathematics
Volume	315
DOIs	https://doi.org/10.1016/j.aim.2017.05.015
State	Published - 31 Jul 2017

Bibliographical note

Funding Information:
Research supported by ISF grants No. 225/13 and 455/15 and ERC Starting Grant No. 713927.

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Diffraction
Dirac comb
Meyer set
Quasicrystal

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10.1016/j.aim.2017.05.015

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Fourier quasicrystals and discreteness of the diffraction spectrum

Abstract

Bibliographical note

Keywords

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