Vol. 48, No. 1, 1973

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Positive-definite distributions and intertwining operators

Roe William Goodman

Vol. 48 (1973), No. 1, 83–91

An example is given of a positive-definite measure μ on the group SL (2,R) which is extremal in the cone of positive-definite measures, but the corresponding unitary representation Lμ is reducible. By considering positive-definite distributions this anomaly disappears, and for an arbitrary Lie group G and positive-definite distribution μ on G a bijection is established between positive-definite distributions on G bounded by μ and positive-definite intertwining operators for the representation Lμ. As an application, cyclic vectors for Lμ are obtained by a simple explicit construction.

Mathematical Subject Classification 2000
Primary: 22E45
Received: 6 June 1972
Revised: 3 November 1972
Published: 1 September 1973
Roe William Goodman