{"paper":{"title":"Discreteness of the spectrum of Schr\\\"odinger operators with non-negative matrix-valued potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Gian Maria Dall'Ara","submitted_at":"2014-02-13T15:27:49Z","abstract_excerpt":"We prove three results giving sufficient and/or necessary conditions for discreteness of the spectrum of Schr\\\"odinger operators with non-negative matrix-valued potentials, i.e., operators acting on $\\psi\\in L^2(\\mathbb{R}^n,\\mathbb{C}^d)$ by the formula $H_V\\psi:=-\\Delta\\psi+V\\psi$, where the potential $V$ takes values in the set of non-negative Hermitian $d\\times d$ matrices. The first theorem provides a characterization of discreteness of the spectrum when the potential $V$ is in a matrix-valued $A_\\infty$ class, thus extending a known result in the scalar case ($d=1$). We also discuss a su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3177","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"}