Vol. 53, No. 2, 1974

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On the Frobenius reciprocity theorem for square-integrable representations

Ray Alden Kunze

Vol. 53 (1974), No. 2, 465–471

In this paper, a global version of the Frobenius reciprocity theorem is established for irreducible square-integrable representations of locally compact unimodular groups. As in the classical compact case, it asserts that certain intertwining spaces are canonically and isometrically isomorphic. The proof is elementary, and the appropriate isomorphism is exhibited explicitely. The essential point is that squareintegrability implies the continuity of functions in certain subspaces of L2 spaces on which the group acts and leads to a characterization of the subspaces in terms of reproducing kernels.

Mathematical Subject Classification 2000
Primary: 22D10
Received: 15 May 1973
Published: 1 August 1974
Ray Alden Kunze