In this paper, a global version
of the Frobenius reciprocity theorem is established for irreducible square-integrable
representations of locally compact unimodular groups. As in the classical compact
case, it asserts that certain intertwining spaces are canonically and isometrically
isomorphic. The proof is elementary, and the appropriate isomorphism is
exhibited explicitely. The essential point is that squareintegrability implies the
continuity of functions in certain subspaces of L2 spaces on which the group acts
and leads to a characterization of the subspaces in terms of reproducing
kernels.
