## Proceedings of the Centre for Mathematics and its Applications

### On the frobenius reciprocity theorem for square integrable representations of nonunimodular groups

Ray A. Kunze

#### 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.

#### Article information

Dates
First available in Project Euclid: 18 November 2014