{"paper":{"title":"Optimal Hardy inequalities for Schr\\\"odinger operators on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Felix Pogorzelski, Matthias Keller, Yehuda Pinchover","submitted_at":"2016-12-13T07:55:01Z","abstract_excerpt":"For a given subcritical discrete Schr\\\"odinger operator $H$ on a weighted infinite graph $X$, we construct a Hardy-weight $w$ which is optimal in the following sense. The operator $H - \\lambda w$ is subcritical in $X$ for all $\\lambda < 1$, null-critical in $X$ for $\\lambda = 1$, and supercritical near any neighborhood of infinity in $X$ for any $\\lambda > 1$. Our results rely on a criticality theory for Schr\\\"odinger operators on general weighted graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04051","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":""},"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"}