Schr\"odinger dispersive estimates for a scaling-critical class of potentials
Analysis of PDEs
2016-08-31 v1
Abstract
We prove a dispersive estimate for the evolution of Schroedinger operators H = -\Delta + V(x) in three dimensions. The potential should belong to the closure of bounded compactly-supported functions with respect to the golbal Kato norm. Some additional spectral conditions are imposed, namely that no resonances or eigenfunctions of H exist anywhere on the positive half-line. The proof is an application of a new version of Wiener's L^1 inversion theorem.
Keywords
Cite
@article{arxiv.1009.5285,
title = {Schr\"odinger dispersive estimates for a scaling-critical class of potentials},
author = {Marius Beceanu and Michael Goldberg},
journal= {arXiv preprint arXiv:1009.5285},
year = {2016}
}
Comments
10 pages