Almost periodic measures and long-range order in Meyer sets
diffraction pattern, computational mathematic, point measure, periodic measure, Bragg peak
The main result of this paper is that the diffraction pattern of any Meyer set with a well-defined autocorrelation has a relatively dense set of Bragg peaks. In the second part of the paper we provide a necessary and sufficient condition for a positive pure point measure to have a continuous Fourier transform. In particular, one can get a necessary and sufficient condition for a point set to have no Bragg peaks in its diffraction.
Strungaru, N. “Almost periodic measures and long range order in Meyer sets”, Discrete and Computational Geometry, 33, 483-505, (2005).
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