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1. CJM 2011 (vol 63 pp. 961)

Bouclet, Jean-Marc
Low Frequency Estimates for Long Range Perturbations in Divergence Form
We prove a uniform control as $ z \rightarrow 0 $ for the resolvent $ (P-z)^{-1} $ of long range perturbations $ P $ of the Euclidean Laplacian in divergence form by combining positive commutator estimates and properties of Riesz transforms. These estimates hold in dimension $d \geq 3 $ when $ P $ is defined on $ \mathbb{R}^d $ and in dimension $ d \geq 2 $ when $ P $ is defined outside a compact obstacle with Dirichlet boundary conditions.

Keywords:resolvent estimates, thresholds, scattering theory, Riesz transform

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