Fourier quasicrystals and discreteness of the diffraction spectrum

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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

Keywords

  • Diffraction
  • Dirac comb
  • Meyer set
  • Quasicrystal

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