{"paper":{"title":"Cubic column relations in 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":"2013-04-21T12:28:58Z","abstract_excerpt":"For the truncated moment problem associated to a complex sequence $\\gamma ^{(2n)}=\\{\\gamma _{ij}\\}_{i,j\\in Z_{+},i+j \\leq 2n}$ to have a representing measure $\\mu $, it is necessary for the moment matrix $M(n)$ to be positive semidefinite, and for the algebraic variety $\\mathcal{V}_{\\gamma}$ to satisfy $\\operatorname{rank}\\;M(n) \\leq \\;$ card$\\;\\mathcal{V}_{\\gamma}$ as well as a consistency condition: the Riesz functional vanishes on every polynomial of degree at most $2n$ that vanishes on $\\mathcal{V}_{\\gamma}$. In previous work with L. Fialkow and M. M\\\"{o}ller, the first-named author proved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5726","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"}