Affine Quantum Harmonic Analysis
Functional Analysis
2021-02-26 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.2102.13006,
title = {Affine Quantum Harmonic Analysis},
author = {Eirik Berge and Stine M. Berge and Franz Luef and Eirik Skrettingland},
journal= {arXiv preprint arXiv:2102.13006},
year = {2021}
}