Quantum harmonic analysis on locally compact groups Article Swipe

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Mathematics Square-integrable function Unimodular matrix Noncommutative harmonic analysis Locally compact space Locally compact group Covariant transformation Pure mathematics Integrable system Compact operator on Hilbert space Affine transformation Heisenberg group Lie group Algebra over a field Compact operator Extension (predicate logic) Mathematical physics Computer science Programming language

Simon Halvdansson ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1016/j.jfa.2023.110096 · OA: W4384023682

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.