{"paper":{"title":"Uniform resolvent estimates for Schr\\\"odinger operator with an inverse-square potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haruya Mizutani, Jiqiang Zheng, Junyong Zhang","submitted_at":"2019-03-12T16:41:40Z","abstract_excerpt":"We study the uniform resolvent estimates for Schr\\\"odinger operator with a Hardy-type singular potential.\n  Let $\\mathcal{L}_V=-\\Delta+V(x)$ where $\\Delta$ is the usual Laplacian on $\\mathbb{R}^n$ and $V(x)=V_0(\\theta) r^{-2}$ where $r=|x|, \\theta=x/|x|$ and $V_0(\\theta)\\in\\mathcal{C}^1(\\mathbb{S}^{n-1})$ is a real function such that the operator $-\\Delta_\\theta+V_0(\\theta)+(n-2)^2/4$ is a strictly positive operator on $L^2(\\mathbb{S}^{n-1})$. We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator $\\mathcal{L}_V$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05040","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.05040/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}