Eberlein decomposition for PV inflation systems

The Dirac combs of primitive Pisot–Vijayaraghavan (PV) inflations on the real line or, more generally, in R d 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 se...

Full description

Saved in:
Bibliographic Details
Published inLetters in mathematical physics Vol. 111; no. 2
Main Authors Baake, Michael, Strungaru, Nicolae
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2021
Springer Nature B.V
Subjects
Complex Systems
Decomposition
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Spectral components
Eberlein decomposition
42A38
52C23
Inflation tilings
Diffraction measure
Online AccessGet full text

Cover

More Information
Summary:The Dirac combs of primitive Pisot–Vijayaraghavan (PV) inflations on the real line or, more generally, in R d 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.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01399-w