{"paper":{"title":"A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Sri Ranga, Daniel Veronese, Kenier Castillo, Marisa Costa","submitted_at":"2013-09-04T12:08:07Z","abstract_excerpt":"The objective of this manuscript is to study directly the Favard type theorem associated with the three term recurrence formula % \\[ R_{n+1}(z) = \\big[(1+ic_{n+1})z+(1-ic_{n+1})\\big] R_{n}(z) - 4 d_{n+1} z R_{n-1}(z), \\quad n \\geq 1, \\] % with $R_{0}(z) =1$ and $R_{1}(z) = (1+ic_{1})z+(1-ic_{1})$, where $\\{c_n\\}_{n=1}^{\\infty}$ is a real sequence and $\\{d_n\\}_{n=1}^{\\infty}$ is a positive chain sequence. We establish that there exists an unique nontrivial probability measure $\\mu$ on the unit circle for which $\\{R_n(z) - 2(1-m_n)R_{n-1}(z)\\}$ gives the sequence of orthogonal polynomials. Here,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0995","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"}