Phase space distributions and harmonic analysis on the Euclidean motion group

Abstract

The Radon transform is at the foundation of tomography whose applications include x-ray and CT-scan technologies, while the Wigner function lies at the root of the phase space space representation of quantum systems, as well as in time-frequency signal analysis. The Wigner function may be characterized by axiomatically representing it as a Radon transform, so that it is natural to bring together the two notions. Our point of view is to bring them together via the harmonic analysis on the Euclidean motion group.