{"paper":{"title":"On the extension of Fredholm determinants to the mixed multidimensional integral operators with regulated kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anton A. Kutsenko","submitted_at":"2016-11-30T14:22:00Z","abstract_excerpt":"We extend the classical trace (and determinant) known for the integral operators $$ ({\\mathcal I}+)\\int_{[0,1)^N}{\\bf A}({\\bf k},{\\bf x}){\\bf u}({\\bf x})d{\\bf x} $$ with matrix-valued kernels ${\\bf A}$ to the operators of the form $$ \\sum_{\\alpha}\\int_{[0,1)^{|\\alpha|}}{\\bf A}({\\bf k},{\\bf x}_{\\alpha}){\\bf u}({\\bf k}_{\\overline{\\alpha}},{\\bf x}_{\\alpha})d{\\bf x}_{\\alpha}, $$ where $\\alpha$ are arbitrary subsets of the set $\\{1,...,N\\}$. Such operators form a Banach algebra containing simultaneously all integral operators of the dimensions $\\leqslant N$. In this sense, it is a largest algebra w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10168","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"}