Diffraction of weighted lattice subsets

Details Diffraction of weighted lattice subsets Diffraction of weighted lattice subsets

2001-06-13

arxiv.org/abs/math/0106111v2

Can. Math. Bulletin 45 (2002) 483 - 498

Mathematics

Metric Geometry

20 pages; revised and expanded version

Scientific paper

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 $\sigma$-compact.

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