Vol. 73, No. 1, 1977

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Square integrable representations and the Fourier algebra of a unimodular group

Giancarlo Mauceri

Vol. 73 (1977), No. 1, 143–154

Let G be a unimodular group, and let λd be the subrepresentation of the left regular representation λ, which is the sum of the square integrable representations. The purpose of this paper is to study the representation λd with special emphasis on the closed subspace Ad(G) of the Fourier algebra A(G) of the group which is generated by the coefficients of λd. In the last part of the paper we study in detail a particular noncompact group for which λ = λd.

Mathematical Subject Classification 2000
Primary: 22D10
Secondary: 43A15
Received: 13 April 1977
Revised: 30 June 1977
Published: 1 November 1977
Giancarlo Mauceri