Pure point diffraction and Poisson summation (Q1689428)

The paper deals with properties of the X-ray diffraction function for regular model sets related to non-periodic structures with long-range order. Such sets, as projections of a subset of a higher-dimensional lattice, are known to have pure point diffraction spectra. The authors prove that the model diffraction formula and Poisson summation formula for the underlying lattice can be derived from each other.