Pure point diffraction and Poisson summation
diffraction, regular model sets, Poisson summation, pure point diffraction
We show that the diffraction formula for regular model sets and the Poisson Summation Formula for the underlying lattice can be derived from one another. This is achieved using Fourier analysis of unbounded Radon measures on locally compact abelian groups, as developed by Argabright and de Lamadrid. We also discuss related diffraction results for certain classes of non-regular so-called weak model sets.
Richard, C. and Strungaru, N. “Pure point diffraction and Poisson summation”, Annales Henri Poincare, Vol 18, No 12, (2017).
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