Diffraction as a Unitary Representation and the Orthogonality of Measures with Respect to the Reflected Eberlein Convolution
Abstract
Abstract We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be placed within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures whose diffractions are mutually singular. We apply this to study dynamical systems, the refined Eberlein decomposition and validity of a Bombieri–Taylor type result in a rather general context. Along the way we also use our approach to (re)prove various characterisations of pure point diffraction.
Fields of Study & Subjects
Numerical methods in inverse problems
Optical and Acousto-Optic Technologies
Publication details
- Journal / source
- Journal of Fourier Analysis and Applications
- Publisher
- Springer Science and Business Media LLC
- Volume
- 32
- Issue
- 4
- Publication date
- 21 July 2026
- Language
- EN