Proceedings of the Centre for Mathematics and its Applications

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

Ray A. Kunze

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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

Source
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

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


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