  We consider the Cauchy problem for the scalar wave equation in the Kerr
geometry for smooth initial data supported outside the event horizon. We prove
that the solutions decay in time in L^\infty_loc. The proof is based on a
representation of the solution as an infinite sum over the angular momentum
modes, each of which is an integral of the energy variable on the real line.
This integral representation involves solutions of the radial and angular ODEs
which arise in the separation of variables.
