Almost periodic measures and Bragg diffraction

In this paper we prove that the cone of positive, positive definite, discrete and strong almost periodic measures over a σ-compact, locally compact Abelian group G has an interesting property: given any positive and positive definite measure μ smaller than some measure in , the strong almost periodi...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 46; no. 12; pp. 125205 - 11
Main Author Strungaru, Nicolae
Format Journal Article
LanguageEnglish
Published IOP Publishing 29.03.2013
Subjects
Bragg diffraction spectrum
Complexity
Diffraction
Mathematical analysis
positive and positive definite measures
strong almost periodic measures
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Summary:In this paper we prove that the cone of positive, positive definite, discrete and strong almost periodic measures over a σ-compact, locally compact Abelian group G has an interesting property: given any positive and positive definite measure μ smaller than some measure in , the strong almost periodic part μS of μ is also in . We then use this result to prove that given a positive-weighted Dirac comb ω with finite local complexity and pure point diffraction, any positive Dirac comb less than ω has either a trivial Bragg spectrum or a relatively dense set of Bragg peaks.
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/12/125205