English

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.

Keywords

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

R2 v1 2026-06-22T13:31:36.277Z