Semiclassical resolvent bounds in dimension two

2016/04/13 by Shapiro, Jacob
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.03852

Abstract

We give an elementary proof of weighted resolvent bounds for semiclassical Schrödinger 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.

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