Une caractérisation de l'algèbre de Fourier pour certains groupes localement compacts

Let G be a separable locally compact group with type-I left regular representation, Gˆ its dual and A(G) its Fourier algebra. We prove an analogue of Parseval's theorem and that the mappingT⟶u(x):=∫GˆTr[T(π)π(x)−1]dμ(π) is an isometric isomorphism of Banach spaces from L1(Gˆ) onto A(G).