## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Miniconference on Harmonic Analysis. M Cowling, C Meaney, and W Moran, eds. Proceedings of the Centre for Mathematical Analysis, v. 15. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1987), 101 - 117

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

#### 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

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416336459

**Mathematical Reviews number (MathSciNet)**

MR935594

**Zentralblatt MATH identifier**

0647.43003

#### Citation

Kunze, Ray A. On the frobenius reciprocity theorem for square integrable representations of nonunimodular groups. Miniconference on Harmonic Analysis, 101--117, Centre for Mathematical Analysis, The Australian National University, Canberra AUS, 1987. https://projecteuclid.org/euclid.pcma/1416336459