{"paper":{"title":"Sums of squares and moment problems in equivariant situations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claus Scheiderer, Jaka Cimpric, Salma Kuhlmann","submitted_at":"2008-08-01T07:59:38Z","abstract_excerpt":"We begin a systematic study of positivity and moment problems in an equivariant setting. Given a reductive group $G$ over $\\R$ acting on an affine $\\R$-variety $V$, we consider the induced dual action on the coordinate ring $\\R[V]$ and on the linear dual space of $\\R[V]$. In this setting, given an invariant closed semialgebraic subset $K$ of $V(\\R)$, we study the problem of representation of invariant nonnegative polynomials on $K$ by invariant sums of squares, and the closely related problem of representation of invariant linear functionals on $\\R[V]$ by invariant measures supported on $K$. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0034","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"}