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Why do (weak) Meyer sets diffract?

Faculty Advisor

Date

2023

Keywords

Meyer sets

Abstract (summary)

Given a weak model set in a locally compact Abelian, group we construct a relatively dense set of common Bragg peaks for all its subsets that have non-trivial Bragg spectrum. Next, we construct a relatively dense set of common norm almost periods for the diffraction, pure point, absolutely continuous and singular continuous spectrum, respectively, of all its subsets. We use the Fibonacci model set to illustrate these phenomena. We extend all these results to arbitrary translation bounded weighted Dirac combs supported within some Meyer set. We complete the paper by discussing extensions of the existence of the generalized Eberlein decomposition for measures supported within some Meyer set.

Publication Information

Strungaru, N. (2023). Why do (weak) Meyer sets diffract? arXiv:2101.10513 [math.FA]. https://arxiv.org/abs/2101.10513

DOI

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Item Type

Article Post-Print

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Embargoed Until:

May 5, 2024

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