  We consider the scalar wave equation in the Kerr geometry for Cauchy data
which is smooth and compactly supported outside the event horizon. We derive an
integral representation which expresses the solution as a superposition of
solutions of the radial and angular ODEs which arise in the separation of
variables. In particular, we prove completeness of the solutions of the
separated ODEs.
  This integral representation is a suitable starting point for a detailed
analysis of the long-time dynamics of scalar waves in the Kerr geometry.
