Abstract Plancherel theorems and a Frobenius reciprocity theorem

A method for obtaining Plancherel theorems for unitary representations of Lie groups via C^∞ vector techniques is studied. The results are used to prove the nonunimodular Plancherel theorem of Moore and to study its convergence. A C^∞ Frobenius reciprocity theorem which generalizes Gelfand's duality theorem is also proven.