Does any one know what the correct formulation of the plancherel theorem should be for Homogeneous spaces. More specific I am looking for a statement like: there is a unique measure in $\mu$ in $\hat G $ such that $L^2(G/H)=\int_{\hat G}^{\oplus}H(\xi)d\mu(\xi)$ and something like a functional $I(f)=\int_{\hat G}^{\oplus}Tr(\xi(f))d\mu $ I will appreciate a lot your help. I am more familiar with the language of C^* algebras so if you can state this in that setting will be even better.
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May be the paper: "MR0444844 (56 #3191) Penney, Richard Abstract Plancherel theorems and a Frobenius reciprocity theorem. J. Functional Analysis 18 (1975), 177–190" is what you are looking for. 

