Pointwise bounds on quasimodes of semiclassical Schrodinger operators in dimension two
Analysis of PDEs
2012-09-14 v1
Abstract
We prove optimal pointwise bounds on quasimodes of semiclassical Schrodinger operators with arbitrary smooth real potentials in dimension two. This end-point estimate was left open in the general study of semiclassical Lp bounds conducted by Koch-Tataru-Zworski. However, we show that their results imply the two dimensional end-point estimate by scaling and localization.
Keywords
Cite
@article{arxiv.1209.2721,
title = {Pointwise bounds on quasimodes of semiclassical Schrodinger operators in dimension two},
author = {Hart F. Smith and Maciej Zworski},
journal= {arXiv preprint arXiv:1209.2721},
year = {2012}
}