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Square integrable representations and the Fourier algebra of a unimodular group

Let G be a unimodular group, and let λ d be the subrepresentation of the left regular representation λ 9 which is the sum of the square integrable representations. The purpose of this paper is to study the representation λ d with special emphasis on the closed subspace A d (G) of the Fourier algebra A(G) of the group which is generated by the coefficients of λ d . In the last part of the paper we study in detail a particular noncompact group for which λ — λ d .