{"paper":{"title":"The Division Algorithm in Sextic Truncated Moment Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Raul E. Curto, Seonguk Yoo","submitted_at":"2016-11-26T17:18:59Z","abstract_excerpt":"For a degree 2n finite sequence of real numbers $\\beta \\equiv \\beta^{(2n)}= \\{ \\beta_{00},\\beta_{10}, \\beta_{01},\\cdots, \\beta_{2n,0}, \\beta_{2n-1,1},\\cdots, \\beta_{1,2n-1},\\beta_{0,2n} \\}$ to have a representing measure $\\mu $, it is necessary for the associated moment matrix $\\mathcal{M}(n)$ to be positive semidefinite, and for the algebraic variety associated to $\\beta $, $\\mathcal{V}_{\\beta} \\equiv \\mathcal{V}(\\mathcal{M}(n))$, to satisfy $\\operatorname{rank} \\mathcal{M}(n)\\leq \\operatorname{card} \\mathcal{V}_{\\beta}$ as well as the following consistency} condition: if a polynomial $p(x,y)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08723","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"}