Admissible vectors and Hilbert algebras. (English) Zbl 1464.43005
Summary: Admissible vectors for unitary representations of locally compact groups are the basis for group frame and covariant coherent state expansions. Main tools in the study of admissible vectors have been Plancherel and central integral decompositions, of applicability only under certain separability and semifiniteness restrictions. In this work, we present a study of admissible vectors in terms of convolution Hilbert algebras valid for arbitrary unitary representations of general locally compact groups.
MSC:
| 43A65 | Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) |
| 47L30 | Abstract operator algebras on Hilbert spaces |
| 46K15 | Hilbert algebras |
Keywords:
locally compact group; unitary representation; admissible vector; Hilbert algebra; frame; coherent stateReferences:
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