Semiclassical resolvent bounds in dimension two

Shapiro, Jacob

doi:10.1090/proc/13758

Semiclassical resolvent bounds in dimension two
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by Jacob Shapiro PDF

Proc. Amer. Math. Soc. 147 (2019), 1999-2008 Request permission

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. This result covers the missing case from the work of Datchev.

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