Resolvent estimates for scalar fields with electromagnetic perturbation

Abstract

In this note we prove some estimates for the resolvent of the operator -Δ perturbed by the differential operator V(x, D) = iα(x) ∙ ∇ + V(x) in ℝ3. This differential operator is of short range type and a compact perturbation of the Laplacian on ℝ3. Also we find estimates in the space-time norm for the solution of the wave equation with such perturbation.