Zero Energy Scattering for One-Dimensional Schr\"odinger Operators and Applications to Dispersive Estimates
Spectral Theory
2015-12-09 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We show that for a one-dimensional Schr\"odinger operator with a potential whose (j+1)'th moment is integrable the j'th derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to improve the known dispersive estimates with integrable time decay for the one-dimensional Schr\"odinger equation in the resonant case.
Keywords
Cite
@article{arxiv.1504.05744,
title = {Zero Energy Scattering for One-Dimensional Schr\"odinger Operators and Applications to Dispersive Estimates},
author = {Iryna Egorova and Markus Holzleitner and Gerald Teschl},
journal= {arXiv preprint arXiv:1504.05744},
year = {2015}
}
Comments
9 pages