{"paper":{"title":"Indeterminacy of the moment problem for symmetric probability measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Hayato Saigo, Hiroki Sako","submitted_at":"2013-02-02T13:59:14Z","abstract_excerpt":"In this paper, the moment problem for symmetric probability measures is characterized in terms of associated sequences called Jacobi sequences $\\{\\omega_n\\}$. A notion named property (SC), which is proved to be a necessary and sufficient condition for the indeterminacy of the moment problem, naturally arises from the viewpoint of finite dimensional approximation for infinite matrices. We prove that the moment problem for q-Gaussian not only for $q>1$ but also for $q<-1$ is indeterminate. We also prove that hyperbolic secant distribution is \"the last probability measure\" which is uniquely deter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0382","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"}