Almost periodic measures and Bragg diffraction

Strungaru, Nicolae

Almost periodic measures and Bragg diffraction

Author

Strungaru, Nicolae

Date

2013

Keywords

Bragg spectrum , Bragg peaks

Abstract (summary)

In this paper we prove that the cone $\mathcal {PDS}(G)$ 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 $\mathcal {PDS}(G)$, the strong almost periodic part μS of μ is also in $\mathcal {PDS}(G)$. 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.

Publication Information

Strungaru, N. “Almost periodic measures and Bragg diffraction”, J. Phys. A: Math. Theor. 46, (2013).

Item Type

Article

Language

English

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