English

Dispersion Estimates for One-Dimensional Schr\"odinger and Klein-Gordon Equations Revisited

Analysis of PDEs 2016-06-30 v2 Mathematical Physics math.MP Spectral Theory

Abstract

We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive dispersion estimates for solutions of the associated Schr\"odinger and Klein-Gordon equations. In particular, we remove the additional decay conditions in the case where a resonance is present at the edge of the continuous spectrum.

Keywords

Cite

@article{arxiv.1411.0021,
  title  = {Dispersion Estimates for One-Dimensional Schr\"odinger and Klein-Gordon Equations Revisited},
  author = {Iryna Egorova and Elena Kopylova and Vladimir Marchenko and Gerald Teschl},
  journal= {arXiv preprint arXiv:1411.0021},
  year   = {2016}
}

Comments

21 pages