Quantitative uniform resolvent estimates

Abstract

We derive quantitative uniform resolvent estimates for Schrödinger operators on the half-line with inverse-square potentials, which provide a sharp behaviour in the limit of large coupling. Our approach is based on a matrix representation of the boundary value of a weighted resolvent. The partial wave decomposition then turns these one-dimensional channel estimates into explicit weighted resolvent estimates for the Laplacian, its inverse-square potential perturbations and for the magnetic Laplacian with an Aharonov--Bohm potential. We also obtain exact Simon-type identities for the imaginary parts of the weighted resolvents of these operators.