Resolvent estimates for the magnetic Schrödinger operator in dimension $n\ge 2$

Abstract

It is well known that the resolvent of the free Schrödinger operator on weighted $L^2$ spaces has norm decaying like ${\lambda }^{-\frac{1}{2}}$ at energy $\lambda$. There are several works proving analogous high-frequency estimates for magnetic Schrödinger operators, with large long or short range potentials, in dimensions $n\ge 3$. We prove that the same estimates remain valid in all dimensions $n\ge 2$.

21 pages