{"paper":{"title":"On Spectral Theory for Schr\\\"odinger Operators with Operator-Valued Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Maxim Zinchenko, Rudi Weikard","submitted_at":"2013-01-04T07:26:26Z","abstract_excerpt":"Given a complex, separable Hilbert space $\\cH$, we consider differential expressions of the type $\\tau = - (d^2/dx^2) + V(x)$, with $x \\in (a,\\infty)$ or $x \\in \\bbR$. Here $V$ denotes a bounded operator-valued potential $V(\\cdot) \\in \\cB(\\cH)$ such that $V(\\cdot)$ is weakly measurable and the operator norm $\\|V(\\cdot)\\|_{\\cB(\\cH)}$ is locally integrable.\n  We consider self-adjoint half-line $L^2$-realizations $H_{\\alpha}$ in $L^2((a,\\infty); dx; \\cH)$ associated with $\\tau$, assuming $a$ to be a regular endpoint necessitating a boundary condition of the type $\\sin(\\alpha)u'(a) + \\cos(\\alpha)u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0682","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"}