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1. CMB 2011 (vol 55 pp. 487)
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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)
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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 Category:43A25 |
3. CMB 2002 (vol 45 pp. 483)
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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 |