{"paper":{"title":"Analysis of Schr\\\"odinger operators with inverse square potentials I: regularity results in 3D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.NA","authors_text":"Eugenie Hunsicker, Hengguang Li, Victor Nistor, Ville Uski","submitted_at":"2012-05-09T23:49:00Z","abstract_excerpt":"Let $V$ be a potential on $\\RR^3$ that is smooth everywhere except at a discrete set $\\maS$ of points, where it has singularities of the form $Z/\\rho^2$, with $\\rho(x) = |x - p|$ for $x$ close to $p$ and $Z$ continuous on $\\RR^3$ with $Z(p) > -1/4$ for $p \\in \\maS$. Also assume that $\\rho$ and $Z$ are smooth outside $\\maS$ and $Z$ is smooth in polar coordinates around each singular point. We either assume that $V$ is periodic or that the set $\\maS$ is finite and $V$ extends to a smooth function on the radial compactification of $\\RR^3$ that is bounded outside a compact set containing $\\maS$. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2124","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}