Quantum harmonic analysis on locally compact groups
Journal article, Peer reviewed
Published version
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Date
2023Metadata
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- Institutt for matematiske fag [2527]
- Publikasjoner fra CRIStin - NTNU [38679]
Original version
Journal of Functional Analysis Volume 285, Issue 8, 15 October 2023, 110096 10.1016/j.jfa.2023.110096Abstract
On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg group. The approach is based on associating to a square integrable representation of the locally compact group two types of convolutions between integrable functions and trace-class operators. In the case of non-unimodular groups these convolutions only are well-defined for admissible operators, which is an extension of the notion of admissible wavelets as has been pointed out recently in the case of the affine group.