Fourier quasicrystals and discreteness of the diffraction spectrum

Nir Lev*, Alexander Olevskii

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 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 languageEnglish
Pages (from-to)1-26
Number of pages26
JournalAdvances in Mathematics
Volume315
DOIs
StatePublished - 31 Jul 2017

Funding

FundersFunder number
Horizon 2020 Framework Programme713927
European Research Council
Israel Science Foundation455/15, 225/13

    Keywords

    • Diffraction
    • Dirac comb
    • Meyer set
    • Quasicrystal

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