{"paper":{"title":"Inequalities and separation for covariant Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hemanth Saratchandran, Ognjen Milatovic","submitted_at":"2018-05-15T11:50:36Z","abstract_excerpt":"We consider a differential expression $L^{\\nabla}_{V}=\\nabla^{\\dagger}\\nabla+V$, where $\\nabla$ is a metric covariant derivative on a Hermitian bundle $E$ over a geodesically complete Riemannian manifold $(M,g)$ with metric $g$, and $V$ is a linear self-adjoint bundle map on $E$. In the language of Everitt and Giertz, the differential expression $L^{\\nabla}_{V}$ is said to be separated in $L^p(E)$ if for all $u\\in L^p(E)$ such that $L^{\\nabla}_{V}u\\in L^p(E)$, we have $Vu\\in L^p(E)$. We give sufficient conditions for $L^{\\nabla}_{V}$ to be separated in $L^2(E)$. We then study the problem of se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06527","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"}