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Note on the set of Bragg peaks with high intensity

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arxiv 1412.7377 v1 pith:ACKGTHRA submitted 2014-12-23 math-ph math.MP

Daniel Lenz , Nicolae Strungaru This is my paper · ORCID
classification math-phmath.MP
keywords positivebraggdefinitehighintensitymeasuresmeyerpeaks
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We consider diffraction of Delone sets in Euclidean space. We show that the set of Bragg peaks with high intensity is always Meyer (if it is relatively dense). We use this to provide a new characterization for Meyer sets in terms of positive and positive definite measures. Our results are based on a careful study of positive definite measures, which may be of interest in its own right.

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  1. Pure point measures with sparse support and sparse Fourier--Bohr support

    math.MG 2019-08 accept novelty 7.0 of 10

    Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.

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