{"paper":{"title":"Orthogonal polynomials on the unit circle: Verblunsky coefficients with some restrictions imposed on a pair of related real sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Sri Ranga, Cleonice F. Bracciali, Daniel O. Veronese, Jairo S. Silva","submitted_at":"2016-08-19T17:50:28Z","abstract_excerpt":"It was shown recently that associated with a pair of real sequences $\\{\\{c_{n}\\}_{n=1}^{\\infty}, \\{d_{n}\\}_{n=1}^{\\infty}\\}$, with $\\{d_{n}\\}_{n=1}^{\\infty}$ a positive chain sequence, there exists a unique nontrivial probability measure $\\mu$ on the unit circle. The Verblunsky coefficients $\\{\\alpha_{n}\\}_{n=0}^{\\infty}$ associated with the orthogonal polynomials with respect to $\\mu$ are given by the relation $$ \\alpha_{n-1}=\\overline{\\tau}_{n-1}\\left[\\frac{1-2m_{n}-ic_{n}}{1-ic_{n}}\\right], \\quad n \\geq 1, $$ where $\\tau_0 = 1$, $\\tau_{n}=\\prod_{k=1}^{n}(1-ic_{k})/(1+ic_{k})$, $n \\geq 1$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08079","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"}