Diffraction of weighted lattice subsets
Michael Baake
Abstract
A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diffraction measure is periodic, with the dual lattice as lattice of periods. This statement remains true in the setting of a locally compact Abelian group that is also σ-compact.
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