Dispersion Estimates for One-dimensional Discrete Schr\"odinger and Wave Equations
Spectral Theory
2015-12-18 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger 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 Schr\"odinger operators which are of independent interest. Most notably we show that the reflection and transmission coefficients belong to the Wiener algebra.
Cite
@article{arxiv.1403.7803,
title = {Dispersion Estimates for One-dimensional Discrete Schr\"odinger and Wave Equations},
author = {Iryna Egorova and Elena Kopylova and Gerald Teschl},
journal= {arXiv preprint arXiv:1403.7803},
year = {2015}
}
Comments
23 pages