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.

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