{"paper":{"title":"On Index Theory for Non-Fredholm Operators: A $(1+1)$-Dimensional Example","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Alan Carey, Denis Potapov, Dima Zanin, Fedor Sukochev, Fritz Gesztesy, Galina Levitina","submitted_at":"2015-09-04T07:51:04Z","abstract_excerpt":"Using the general formalism of [12], a study of index theory for non-Fredholm operators was initiated in [9]. Natural examples arise from $(1+1)$-dimensional differential operators using the model operator $D_A$ in $L^2(\\mathbb{R}^2; dt dx)$ of the type $D_A = (d/dt) + A$, where $A = \\int^{\\oplus}_{\\mathbb{R}} dt \\, A(t)$, and the family of self-adjoint operators $A(t)$ in $L^2(\\mathbb{R}; dx)$ is explicitly given by $A(t) = - i (d/dx) + \\theta(t) \\phi(\\cdot)$, $t \\in \\mathbb{R}$. Here $\\phi: \\mathbb{R} \\to \\mathbb{R}$ has to be integrable on $\\mathbb{R}$ and $\\theta: \\mathbb{R} \\to \\mathbb{R}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01356","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"}