On the Bragg Diffraction Spectra of a Meyer Set

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 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.

32 pages

References in corpus (1)

• Pure point diffraction and cut and project schemes for measures: The smooth case

Cited by in corpus (11)

• On the Fourier Analysis of Measures with Meyer Set Support
• On Weighted Dirac Combs Supported Inside Model Sets
• On a Family of Random Noble Means Substitutions
• On arithmetic progressions in model sets
• Model sets with precompact Borel windows
• Inflation versus projection sets in aperiodic systems: The role of the window in averaging and diffraction
• On the Fourier Transformability of Strongly Almost Periodic Measures
• A note on measures vanishing at infinity
• Meyer sets, topological eigenvalues, and Cantor fiber bundles
• Why do Meyer sets diffract?
• Fourier Transformable Measures with Meyer set support and their lift to the cut and project scheme