Diffraction of Weighted Lattice Subsets

Baake, Michael

Canadian mathematical bulletin, Tome 45 (2002) no. 4, pp. 483-498

Résumé

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.

Détail

DOI : 10.4153/CMB-2002-050-2

Mots-clés : 52C07, 43A25, 52C23, 43A05, diffraction, Dirac combs, lattice subsets, homometric sets

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