{"paper":{"title":"A determinant characterization of moment sequences with finitely many mass-points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CA","authors_text":"Christian Berg, Ryszard Szwarc","submitted_at":"2014-05-28T15:06:30Z","abstract_excerpt":"To a sequence (s_n)_{n\\ge 0} of real numbers we associate the sequence of Hankel matrices \\mathcal H_n=(s_{i+j}),0\\le i,j \\le n. We prove that if the corresponding sequence of Hankel determinants D_n=\\det\\mathcal H_n satisfy D_n>0 for n<n_0 while D_n=0 for n\\ge n_0, then all Hankel matrices are positive semi-definite, and in particular (s_n) is the sequence of moments of a discrete measure concentrated in n_0 points on the real line. We stress that the conditions D_n\\ge 0 for all n do not imply the positive semi-definiteness of the Hankel matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7267","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"}