{"paper":{"title":"Initial Value Problems and Weyl--Titchmarsh 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":"2011-09-08T02:24:55Z","abstract_excerpt":"We develop Weyl-Titchmarsh theory for self-adjoint Schr\\\"odinger operators $H_{\\alpha}$ in $L^2((a,b);dx;\\cH)$ associated with the operator-valued differential expression $\\tau =-(d^2/dx^2)+V(\\cdot)$, with $V:(a,b)\\to\\cB(\\cH)$, and $\\cH$ a complex, separable Hilbert space. We assume regularity of the left endpoint $a$ and the limit point case at the right endpoint $b$. In addition, the bounded self-adjoint operator $\\alpha= \\alpha^* \\in \\cB(\\cH)$ is used to parametrize the self-adjoint boundary condition at the left endpoint $a$ of the type $$ \\sin(\\alpha)u'(a)+\\cos(\\alpha)u(a)=0, $$ with $u$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1613","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"}