Semiclassical resolvent bounds in dimension two
Analysis of PDEs
2017-06-06 v3
Abstract
We give an elementary proof of weighted resolvent bounds for semiclassical Schr\"odinger operators in dimension two. We require the potential function to be Lipschitz with long range decay. The resolvent norm grows exponentially in the inverse semiclassical parameter, but near infinity it grows linearly. Our result covers the missing case from the work of Datchev.
Cite
@article{arxiv.1604.03852,
title = {Semiclassical resolvent bounds in dimension two},
author = {Jacob Shapiro},
journal= {arXiv preprint arXiv:1604.03852},
year = {2017}
}
Comments
8 pages