We show that for a one-dimensional Schrodinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive dispersion est
imates for solutions of the associated Schrodinger and Klein-Gordon equations. In particular, we remove the additional decay conditions in the case where a resonance is present at the edge of the continuous spectrum.
