Vol. 7, No. 7, 2014

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Resolvent estimates for the magnetic Schrödinger operator

Georgi Vodev

Vol. 7 (2014), No. 7, 1639–1648
Abstract

We prove optimal high-frequency resolvent estimates for self-adjoint operators of the form

$G=-\Delta +ib\left(x\right)\cdot \nabla +i\nabla \cdot b\left(x\right)+V\left(x\right)$

on ${L}^{2}\left({ℝ}^{n}\right)$, $n\ge 3$, where $b\left(x\right)$ and $V\left(x\right)$ are large magnetic and electric potentials, respectively.

Keywords
magnetic potential, resolvent estimates
Primary: 47A10