Note on the set of Bragg peaks with high intensity
autocorrelation, discrete Fourier transform, Bragg peak, compact abelian group, pure point
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.
Lenz, D. and Strungaru, N. “Note on the set of Bragg peaks with high intensity”, Annales Henri Poincare, Volume 17, Number 3, (2016).
All Rights Reserved