Dispersion Estimates for One-Dimensional Schr\"odinger and Klein-Gordon   Equations Revisited
  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. 
Iryna Egorova, Elena Kopylova, Vladimir Marchenko, and Gerald Teschl
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