{"paper":{"title":"Inversion formula and range conditions for a vector multi-interval finite Hilbert transform in $L^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander Katsevich, Alexander Tovbis, Marco Bertola","submitted_at":"2018-06-01T16:50:30Z","abstract_excerpt":"Given $n$ disjoint intervals $I_j$, on $\\mathbb R$ together with $n$ functions $\\psi_j\\in L^2(I_j)$, $j=1,\\dots n$, and an $n\\times n$ matrix $\\Theta$, the problem is to find an $L^2$ solution $\\vec \\varphi= {\\rm Col} (\\varphi_1,\\dots, \\varphi_n)$, $\\varphi_j \\in L^2(I_j)$ to the linear system $\\chi\\Theta \\mathcal H \\vec \\varphi = \\vec\\psi$, where $\\mathcal H = {\\rm diag} (\\mathcal H_1 ,\\dots, \\mathcal H_n)$ is a matrix of finite Hilbert transforms and $\\chi=\\text{diag}(\\chi_1,\\dots,\\chi_n)$ is a matrix of the corresponding characteristic functions on $I_j$, and $\\vec \\psi={\\rm Col} (\\psi_1,\\d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00436","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"}