{"paper":{"title":"Sturm-Liouville boundary value problems with operator potentials and unitary equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Hagen Neidhardt, Mark Malamud","submitted_at":"2011-02-18T14:56:46Z","abstract_excerpt":"Consider the minimal Sturm-Liouville operator $A = A_{\\rm min}$ generated by the differential expression $\\mathcal{A} := -\\frac{d^2}{dt^2} + T$ in the Hilbert space $L^2(\\mathbb{R}_+,\\mathcal{H})$ where $T = T^*\\ge 0$ in $\\mathcal{H}$. We investigate the absolutely continuous parts of different self-adjoint realizations of $\\mathcal{A}$. In particular, we show that Dirichlet and Neumann realizations, $A^D$ and $A^N$, are absolutely continuous and unitary equivalent to each other and to the absolutely continuous part of the Krein realization. Moreover, if $\\inf\\sigma_{ess}(T) = \\inf\\sigma(T) \\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3849","kind":"arxiv","version":3},"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"}