  We show that for a one-dimensional Schr\"odinger 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 estimates for solutions of the associated Schr\"odinger 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.
