Dispersion estimates for one-dimensional discrete Schrodinger and wave equations

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schrodinger 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 Schrodinger operators which are of independent interest. Most notably we show that the reflection and transmission coefficients belong to the Wiener algebra.