Canad. Math. Bull. 45(2002), 483-498
Printed: Dec 2002
A Dirac comb of point measures in Euclidean space with bounded
complex weights that is supported on a lattice $\varGamma$ 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
$\varGamma^*$ as lattice of periods. This statement remains true
in the setting of a locally compact Abelian group whose topology
has a countable base.
diffraction, Dirac combs, lattice subsets, homometric sets
52C07 - Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]
43A25 - Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
52C23 - Quasicrystals, aperiodic tilings
43A05 - Measures on groups and semigroups, etc.