{"paper":{"title":"A Jost-Pais-type reduction of Fredholm determinants and some applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.FA","authors_text":"Alan Carey, Denis Potapov, Fedor Sukochev, Fritz Gesztesy, Yuri Tomilov","submitted_at":"2014-04-03T00:36:44Z","abstract_excerpt":"We study the analog of semi-separable integral kernels in $\\cH$ of the type {equation*} K(x,x')={cases} F_1(x)G_1(x'), & a<x'< x< b, \\\\ F_2(x)G_2(x'), & a<x<x'<b, {cases} {equation*} where $-\\infty\\leq a<b\\leq \\infty$, and for a.e.\\ $x \\in (a,b)$, $F_j (x) \\in \\cB_2(\\cH_j,\\cH)$ and $G_j(x) \\in \\cB_2(\\cH,\\cH_j)$ such that $F_j(\\cdot)$ and $G_j(\\cdot)$ are uniformly measurable, and {equation*} \\|F_j(\\cdot)\\|_{\\cB_2(\\cH_j,\\cH)} \\in L^2((a,b)), \\; \\|G_j (\\cdot)\\|_{\\cB_2(\\cH,\\cH_j)} \\in L^2((a,b)), \\quad j=1,2, {equation*} with $\\cH$ and $\\cH_j$, $j=1,2$, complex, separable Hilbert spaces. Assuming"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0739","kind":"arxiv","version":2},"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"}