On weighted Dirac combs supported inside model sets
Author
Faculty Advisor
Date
2014
Keywords
Meyer sets, model sets, almost periodic measures, diffraction, Bragg spectra
Abstract (summary)
In this paper we prove that given a weakly almost periodic measure μ supported inside some model set $\Lambda (W)$ with closed window W, then the strongly almost periodic component ${{\mu }_{S}}$ and the null weakly almost periodic component μ0 are both supported inside $\Lambda (W)$. As a consequence we prove that given any translation bounded measure ω, supported inside some model set, then each of the pure point diffraction spectrum ${{\hat{\gamma }}_{{\rm pp}}}$ and the continuous diffraction spectrum ${{\hat{\gamma }}_{c}}$ is either trivial or has a relatively dense support.
Publication Information
Strungaru, N. “On weighted Dirac combs supported inside model sets”, J. Phys. A: Math. Theor. 47 (2014).
Notes
Item Type
Article
Language
English
Rights
All Rights Reserved