Geodesic
Dispersion estimates for one-dimensional Schr\"odinger and Klein--Gordon equations revisited
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 3, pp. 391-415

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It is shown that for a one-dimensional Schrödinger operator with a potential whose first moment is integrable the elements of the scattering matrix are in the unital Wiener algebra of functions with integrable Fourier transforms. This is then used to derive dispersion estimates for solutions of the associated Schrödinger and Klein–Gordon equations. In particular, the additional decay conditions are removed in the case where a resonance is present at the edge of the continuous spectrum. Bibliography: 29 titles.
Keywords: Schrödinger equation, dispersion estimates, scattering.
Mots-clés : Klein–Gordon equation 
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I. E. Egorova; E. A. Kopylova; V. A. Marchenko; G. Teschl. Dispersion estimates for one-dimensional Schr\"odinger and Klein--Gordon equations revisited. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 3, pp. 391-415. http://geodesic.mathdoc.fr/item/RM_2016_71_3_a0/