Exponential lower resolvent bounds far away from trapped sets
Analysis of PDEs
2020-07-06 v3 Classical Analysis and ODEs
Spectral Theory
Abstract
We give examples of semiclassical Schr\"odinger operators with exponentially large cutoff resolvent norms, even when the supports of the cutoff and potential are very far apart. The examples are radial, which allows us to analyze the resolvent kernel in detail using ordinary differential equation techniques. In particular, we identify a threshold spatial radius where the resolvent behavior changes. We apply these results to wave equations with radial wavespeed, identifying a corresponding threshold radius at which wave decay properties change.
Cite
@article{arxiv.1705.03976,
title = {Exponential lower resolvent bounds far away from trapped sets},
author = {Kiril Datchev and Long Jin},
journal= {arXiv preprint arXiv:1705.03976},
year = {2020}
}
Comments
24 pages, 5 figures. Minor corrections and updates to the references