Square integrable representations of unimodular groups
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- by David S. Shucker PDF
- Proc. Amer. Math. Soc. 89 (1983), 169-172 Request permission
Abstract:
An elementary proof is given showing that if a continuous irreducible unitary representation of a locally compact unimodular group $G$ has one nontrivial square integrable matrix entry, then all its matrix entries are square integrable. This result was first proved by R. Godement.References
- Roger Godement, Sur les relations d’orthogonalité de V. Bargmann. I. Résultats préliminaires, C. R. Acad. Sci. Paris 225 (1947), 521–523 (French). MR 21944
- Roger Godement, Sur les relations d’orthogonalité de V. Bargmann. II. Démonstration générale, C. R. Acad. Sci. Paris 225 (1947), 657–659 (French). MR 21945
- Jacques Dixmier, $C^*$-algebras, North-Holland Mathematical Library, Vol. 15, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Translated from the French by Francis Jellett. MR 0458185
- Armand Borel, Représentations de groupes localement compacts, Lecture Notes in Mathematics, Vol. 276, Springer-Verlag, Berlin-New York, 1972. MR 0414779
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 169-172
- MSC: Primary 22D10
- DOI: https://doi.org/10.1090/S0002-9939-1983-0706534-4
- MathSciNet review: 706534