Affine Quantum Harmonic Analysis

Eirik Berge, Stine M. Berge, Franz Luef, Eirik Skrettingland

Published 2021-02-25Version 1

We develop a quantum harmonic analysis framework for the affine group. This encapsulates several examples in the literature such as affine localization operators, covariant integral quantizations, and affine quadratic time-frequency representations. In the process, we develop a notion of admissibility for operators and extend well known results to the operator setting. A major theme of the paper is the interaction between operator convolutions, affine Weyl quantization, and admissibility.