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2 results

  • A Short Proof of the Characterization of Model Sets by Almost Automorphy

  • Jean-Baptiste Aujogue
  • Journal:
    Canadian Mathematical Bulletin / Volume 61 / Issue 3 / 01 September 2018
    Published online by Cambridge University Press:
    20 November 2018, pp. 464-472
    Print publication:
    01 September 2018
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  • The aim of this note is to provide a conceptually simple demonstration of the fact that repetitive model sets are characterized as the repetitive Meyer sets with an almost automorphic associated dynamical system.

  • On the Bragg Diffraction Spectra of a Meyer Set

  • Nicolae Strungaru
  • Journal:
    Canadian Journal of Mathematics / Volume 65 / Issue 3 / 01 June 2013
    Published online by Cambridge University Press:
    20 November 2018, pp. 675-701
    Print publication:
    01 June 2013
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  • Meyer sets have a relatively dense set of Bragg peaks, and for this reason they may be considered as basic mathematical examples of (aperiodic) crystals. In this paper we investigate the pure point part of the diffraction of Meyer sets in more detail. The results are of two kinds. First, we show that, given a Meyer set and any positive intensity $a$ less than the maximum intensity of its Bragg peaks, the set of Bragg peaks whose intensity exceeds $a$ is itself a Meyer set (in the Fourier space). Second, we show that if a Meyer set is modified by addition and removal of points in such a way that its density is not altered too much (the allowable amount being given explicitly as a proportion of the original density), then the newly obtained set still has a relatively dense set of Bragg peaks.