JournalsjstVol. 5, No. 4pp. 663–696

Dispersion estimates for one-dimensional discrete Schrödinger and wave equations

  • Iryna Egorova

    Universität Wien, Austria
  • Elena A. Kopylova

    Universität Wien, Austria
  • Gerald Teschl

    Universität Wien, Austria
Dispersion estimates for one-dimensional discrete Schrödinger and wave equations cover

Abstract

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 reection and transmission coefficients belong to the Wiener algebra.

Cite this article

Iryna Egorova, Elena A. Kopylova, Gerald Teschl, Dispersion estimates for one-dimensional discrete Schrödinger and wave equations. J. Spectr. Theory 5 (2015), no. 4, pp. 663–696

DOI 10.4171/JST/110