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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Square integrable representations of unimodular groups


Author: David S. Shucker
Journal: Proc. Amer. Math. Soc. 89 (1983), 169-172
MSC: Primary 22D10
MathSciNet review: 706534
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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 [Enhancements On Off] (What's this?)

  • [1] Roger Godement, Sur les relations d’orthogonalité de V. Bargmann. I. Résultats préliminaires, C. R. Acad. Sci. Paris 225 (1947), 521–523 (French). MR 0021944 (9,134a)
  • [2] Roger Godement, Sur les relations d’orthogonalité de V. Bargmann. II. Démonstration générale, C. R. Acad. Sci. Paris 225 (1947), 657–659 (French). MR 0021945 (9,134b)
  • [3] Jacques Dixmier, 𝐶*-algebras, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Translated from the French by Francis Jellett; North-Holland Mathematical Library, Vol. 15. MR 0458185 (56 #16388)
  • [4] Armand Borel, Représentations de groupes localement compacts, Lecture Notes in Mathematics, Vol. 276, Springer-Verlag, Berlin-New York, 1972. MR 0414779 (54 #2871)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0706534-4
PII: S 0002-9939(1983)0706534-4
Article copyright: © Copyright 1983 American Mathematical Society