Eberlein decomposition for PV inflation systems

Author
Baake, Michael
Strungaru, Nicolae
Faculty Advisor
Date
2021
Keywords
inflation tilings , diffraction measure , Eberlein decomposition , spectral components
Abstract (summary)
The Dirac combs of primitive Pisot–Vijayaraghavan (PV) inflations on the real line or, more generally, in Rd are analysed. We construct a mean-orthogonal splitting for such Dirac combs that leads to the classic Eberlein decomposition on the level of the pair correlation measures, and thus to the separation of pure point versus continuous spectral components in the corresponding diffraction measures. This is illustrated with two guiding examples, and an extension to more general systems with randomness is outlined.
Publication Information
Baake, M., Strungaru, N. (2021). Eberlein decomposition for PV inflation systems. Letters in Mathematical Physics 111(2),59. https://doi.org/10.1007/s11005-021-01399-w
DOI
Notes
Item Type
Article
Language
English
Rights
Attribution (CC BY)