{"paper":{"title":"BV spaces and the perimeters related to Schrodinger operators with inverse-square potentials and applications to the rank-one theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jizheng Huang, Pengtao Li, Yang Han, Yu Liu","submitted_at":"2022-03-31T03:09:31Z","abstract_excerpt":"For $a \\ge - {( \\frac{{d}}{2}- 1)^2} $ and $2\\sigma= {{d - 2}}-( {{{(d - 2)}^2} + 4a})^{1/2}$, let $$\\begin{cases}\\mathcal{H}_{a}= - \\Delta + \\frac{a} {{{{ | x |}^2}}},\\\\ \\mathcal{\\widetilde{H}}_{\\sigma}= 2\\big( { - \\Delta + \\frac{{{\\sigma ^2}}} {{{{ | x |}^2}}}}\\big)\\end{cases}$$ be two Schr\\\"odinger operators with inverse-square potentials. In this paper, on the domain $\\Omega \\subset {\\mathbb {R}^d}\\backslash \\{ 0\\}, d\\geq 2,$ %apart from the origin, the ${\\mathcal{H} _a}$-BV space $\\mathcal{B} {\\mathcal{V} _{{\\mathcal{H} _a}}}(\\Omega )$ and the ${\\mathcal{\\widetilde{H}}_{\\sigma}}$-BV space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.16770","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.16770/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"}