J. Spectr. Theory 5, 663-696 (2015) [DOI: 10.4171/JST/110]

Dispersion Estimates for One-Dimensional Discrete Schrödinger and Wave Equations

Iryna Egorova, Elena Kopylova, and Gerald Teschl

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schrödinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide new results concerning scattering for one-dimensional discrete perturbed Schrödinger operators which are of independent interest. Most notably we show that the reflection and transmission coefficients belong to the Wiener algebra.

MSC2010: Primary 35Q41, 81Q15; Secondary 39A12, 39A70
Keywords: Discrete Schrödinger equation, discrete wave equation, dispersive decay, scattering theory

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