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Diffraction of Weighted Lattice Subsets
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- Journal:
- Canadian Mathematical Bulletin / Volume 45 / Issue 4 / 01 December 2002
- Published online by Cambridge University Press:
- 20 November 2018, pp. 483-498
- Print publication:
- 01 December 2002
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- Article
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A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice
$\Gamma$ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniformlattice Dirac comb, and its diffraction measure is periodic, with the dual lattice 
${{\Gamma }^{*}}$ as lattice of periods. This statement remains true in the setting of a locally compact Abelian group whose topology has a countable base.
