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Diffraction of Weighted Lattice Subsets

Published online by Cambridge University Press:  20 November 2018

Michael Baake
Michael Baake*
Affiliation:
Institut für Mathematik Universität Greifswald Jahnstr. 15a 17487 Greifswald Germany, email: mbaake@uni-greifswald.de
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Abstract

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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.

Keywords

52C0743A2552C2343A05diffractionDirac combslattice subsetshomometric sets

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 4 , 01 December 2002, pp. 483 - 498
Copyright
Copyright © Canadian Mathematical Society 2002

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