{"paper":{"title":"Trace Formulas for a Class of non-Fredholm Operators: A Review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Alan Carey, Denis Potapov, Dmitriy Zanin, Fedor Sukochev, Fritz Gesztesy, Galina Levitina, Harald Grosse","submitted_at":"2016-10-17T02:38:11Z","abstract_excerpt":"We review previous work on spectral flow in connection with certain self-adjoint model operators $\\{A(t)\\}_{t\\in \\mathbb{R}}$ on a Hilbert space $\\mathcal{H}$, joining endpoints $A_\\pm$, and the index of the operator $D_{A}^{}= (d/d t) + A$ acting in $L^2(\\mathbb{R}; \\mathcal{H})$, where $A$ denotes the operator of multiplication $(A f)(t) = A(t)f(t)$. In this article we review what is known when these operators have some essential spectrum and describe some new results in terms of associated spectral shift functions.\n  We are especially interested in extensions to non-Fredholm situations, rep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04954","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"}