Exponential Lower Bounds for Quasimodes of Semiclassical Schr\"{o}dinger Operators
Analysis of PDEs
2009-07-31 v3
Abstract
We prove quantitative unique continuation results for the semiclassical Schrodinger operator on smooth, compact domains. These take the form of exponentially decreasing (in h) local L^{2} lower bounds for exponentially precise quasimodes. We also show that these lower bounds are sharp in h, and that, moreover, the hypothesized quasimode accuracy is also sharp.
Keywords
Cite
@article{arxiv.0808.3035,
title = {Exponential Lower Bounds for Quasimodes of Semiclassical Schr\"{o}dinger Operators},
author = {Michael VanValkenburgh},
journal= {arXiv preprint arXiv:0808.3035},
year = {2009}
}
Comments
14 pages, no figures; cosmetic changes. Final version, to appear in Mathematical Research Letters