{"paper":{"title":"The moment problem with bounded density","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Jean B. Lasserre","submitted_at":"2006-07-19T14:17:43Z","abstract_excerpt":"Let $\\mu$ be a given Borel measure on $\\K\\subseteq\\R^n$ and let $y=(y_\\alpha)$, $\\alpha\\in\\N^n$, be a given sequence. We provide several conditions linking $y$ and the moment sequence $z=(z_\\alpha)$ of $\\mu$, for $y$ to be the moment sequence of a Borel measure $\\nu$ on $\\K$ which is absolutely continuous with respect to $\\mu$ and such that its density is in $L_\\infty(\\K,\\mu)$. The conditions are necessary and sufficient if $\\K$ is a compact basic semi-algebraic set, and sufficient if $\\K\\equiv\\R^n$. Moreover, arbitrary finitely many of these conditions can be checked by solving either a semid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607463","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"}