1. CMB 2011 (vol 55 pp. 487)
|Weighted Model Sets and their Higher Point-Correlations|
Examples of distinct weighted model sets with equal $2,3,4, 5$-point correlations are given.
Keywords:model sets, correlations, diffraction
Categories:52C23, 51P05, 74E15, 60G55
2. CMB 2011 (vol 54 pp. 544)
|Positive Definite Measures with Discrete Fourier Transform and Pure Point Diffraction|
In this paper we characterize the positive definite measures with discrete Fourier transform. As an application we provide a characterization of pure point diffraction in locally compact Abelian groups.
Keywords:pure point diffraction, positive definite measure, Fourier transform of measures
3. 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