Abstract
In the unimodular case, the Frobenius reciprocity theorem for irreducible square integrable representations asserts that certain intertwining spaces are canonically isomorphic; the essential analytic point is that square integrability implies the continuity of functions in particular subspaces of $L^2$ spaces on which the group acts and leads to a characterization of these subspaces in terms of reproducing kernels. In the nonunimodular case this is no longer true. There is a canonical isomorphism between proper subspaces of the intertwining spaces, one of which is uniformly dense in the full intertwining space.
Information
Published: 1 January 1987
First available in Project Euclid: 18 November 2014
zbMATH: 0647.43003
MathSciNet: MR935594
Rights: Copyright © 1987, Centre for Mathematical Analysis, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.