Quantitative uniform resolvent estimates
偏微分方程分析
2026-06-25 v1 数学物理
谱理论
摘要
We derive quantitative uniform resolvent estimates for Schr\"odinger 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.
引用
@article{arxiv.2606.26825,
title = {Quantitative uniform resolvent estimates},
author = {Piero D'Ancona and Jérémy Faupin and David Krejcirik},
journal= {arXiv preprint arXiv:2606.26825},
year = {2026}
}