Almost periodic measures and Bragg diffraction
Author
Faculty Advisor
Date
2013
Keywords
Bragg spectrum, Bragg peaks
Abstract (summary)
In this paper we prove that the cone 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 PDS(G), the strong almost periodic part μS of μ is also in 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).
Notes
Item Type
Article
Language
English
Rights
All Rights Reserved