Russian Math. Surveys 71, 3-26 (2016) [DOI: 10.4213/rm9708]

Dispersion Estimates for One-Dimensional Schrödinger and Klein-Gordon Equations Revisited

Iryna Egorova, Elena Kopylova, Vladimir Aleksandrovich Marchenko, and Gerald Teschl

We show that for a one-dimensional Schrödinger 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 Schrödinger 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.

MSC2010: Primary 35L10, 34L25; Secondary 81U30, 81Q15
Keywords: Schrödinger equation, Klein-Gordon equation, dispersive estimates, scattering

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