Diffraction of weighted lattice subsets

Michael Baake

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Diffraction of weighted lattice subsets

Michael Baake

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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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Michael Baake. 2002-02-13. Diffraction of weighted lattice subsets. https://arxiv.org/abs/math/0106111

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