1. CMB 2002 (vol 45 pp. 483)
|Diffraction of Weighted Lattice Subsets |
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.
Keywords:diffraction, Dirac combs, lattice subsets, homometric sets
Categories:52C07, 43A25, 52C23, 43A05