Almost periodic measures and Bragg diffraction

Author
Strungaru, Nicolae
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).
Article
English