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On the Bragg Diffraction Spectra of a Meyer Set

  Published:2012-12-04
 Printed: Jun 2013
  • Nicolae Strungaru,
    Department of Mathematical Sciences, Grant MacEwan University, Edmonton, AB, T5J 4S2
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Abstract

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.
Keywords: diffraction, Meyer set, Bragg peaks diffraction, Meyer set, Bragg peaks
MSC Classifications: 52C23 show english descriptions Quasicrystals, aperiodic tilings 52C23 - Quasicrystals, aperiodic tilings
 

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