{"paper":{"title":"Shnol-type theorem for the Agmon ground state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Siegfried Beckus, Yehuda Pinchover","submitted_at":"2017-06-15T13:52:13Z","abstract_excerpt":"Let $H$ be a Schr\\\"odinger operator defined on a noncompact Riemannian manifold $\\Omega$, and let $W\\in L^\\infty(\\Omega;\\mathbb{R})$. Suppose that the operator $H+W$ is critical in $\\Omega$, and let $\\varphi$ be the corresponding Agmon ground state. We prove that if $u$ is a generalized eigenfunction of $H$ satisfying $|u|\\leq \\varphi$ in $\\Omega$, then the corresponding eigenvalue is in the spectrum of $H$. The conclusion also holds true if for some $K\\Subset \\Omega$ the operator $H$ admits a positive solution in $\\tilde{\\Omega}=\\Omega\\setminus K$, and $|u|\\leq \\psi$ in $\\tilde{\\Omega}$, wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04869","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"}