{"paper":{"title":"The Moment Problem for Continuous Positive Semidefinite Linear functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ebrahim Samei, Mehdi Ghasemi, Salma Kuhlmann","submitted_at":"2010-10-14T00:12:33Z","abstract_excerpt":"Let $\\tau$ be a locally convex topology on the countable dimensional polynomial $\\reals$-algebra $\\rx:=\\reals[X_1,...,X_n]$. Let $K$ be a closed subset of $\\reals^n$, and let $M:=M_{\\{g_1, ... g_s\\}}$ be a finitely generated quadratic module in $\\rx$. We investigate the following question: When is the cone $\\Pos(K)$ (of polynomials nonnegative on $K$) included in the closure of $M$? We give an interpretation of this inclusion with respect to representing continuous linear functionals by measures. We discuss several examples; we compute the closure of $M=\\sos$ with respect to weighted norm-$p$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2796","kind":"arxiv","version":5},"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"}