{"paper":{"title":"Donoghue-Type $m$-Functions for Schr\\\"odinger Operators with Operator-Valued Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Fritz Gesztesy, Maxim Zinchenko, Rudi Weikard, Sergey N. Naboko","submitted_at":"2015-06-21T05:44:27Z","abstract_excerpt":"Given a complex, separable Hilbert space $\\mathcal{H}$, we consider self-adjoint $L^2$-realizations of differential expressions $\\tau = - (d^2/dx^2) I_{\\mathcal{H}} + V(x)$, on half-lines and on the real line (assuming the limit-point property of $\\tau$ at $\\pm \\infty$). Here $V$ denotes a bounded operator-valued potential $V(\\cdot) \\in \\mathcal{B}(\\mathcal{H})$ such that $V(\\cdot)$ is weakly measurable, the operator norm $\\|V(\\cdot)\\|_{\\mathcal{B}(\\mathcal{H})}$ is locally integrable, and $V(\\cdot) = V(\\cdot)^*$ a.e.\n  In a nutshell, a Donoghue-type $m$-function $M_{A,\\mathcal{N}_i}^{Do}(\\cdo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06324","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"}