Geodesic
Diffraction of Weighted Lattice Subsets
Canadian mathematical bulletin, Tome 45 (2002) no. 4, pp. 483-498

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DOI

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.
DOI : 10.4153/CMB-2002-050-2
Mots-clés : 52C07, 43A25, 52C23, 43A05, diffraction, Dirac combs, lattice subsets, homometric sets 
Baake, Michael. Diffraction of Weighted Lattice Subsets. Canadian mathematical bulletin, Tome 45 (2002) no. 4, pp. 483-498. doi: 10.4153/CMB-2002-050-2
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     author = {Baake, Michael},
     title = {Diffraction of {Weighted} {Lattice} {Subsets}},
     journal = {Canadian mathematical bulletin},
     pages = {483--498},
     year = {2002},
     volume = {45},
     number = {4},
     doi = {10.4153/CMB-2002-050-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-050-2/}
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