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.
