Fourier quasicrystals and discreteness of the diffraction spectrum

Nir Lev, Alexander Olevskii

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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
StatePublished - 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.


  • Diffraction
  • Dirac comb
  • Meyer set
  • Quasicrystal


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