On weighted Dirac combs supported inside model sets

Author
Strungaru, Nicolae
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).
DOI
Notes
Item Type
Article
Language
English
Rights
All Rights Reserved