  A generalization of the mode stability result of Whiting (1989) for the
Teukolsky equation is proved for the case of real frequencies. The main result
of the paper states that a separated solution of the Teukolsky equation
governing massless test fields on the Kerr spacetime, which is purely outgoing
at infinity, and purely ingoing at the horizon, must vanish. This has the
consequence, that for real frequencies, there are linearly independent
fundamental solutions of the radial Teukolsky equation which are purely ingoing
at the horizon, and purely outgoing at infinity, respectively. This fact yields
a representation formula for solutions of the inhomogenous Teukolsky equation.
