ABSTRACT
In this chapter we present the basic concepts in the theory of unitary representations of locally compact groups and derive a few fundamental results: Schur’s lemma, the correspondence between unitary representations of G and ∗-representations of L1(G), and the Gelfand-Raikov existence theorem for irreducible representations. The main tool in proving the latter theorem is the connection between cyclic representations and functions of positive type, an extremely fertile idea that will play a role in a number of places later in the book.
