{"paper":{"title":"Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alagacone Sri Ranga, Anbhu Swaminathan, Cleonice F. Bracciali","submitted_at":"2014-06-03T14:09:29Z","abstract_excerpt":"When a nontrivial measure $\\mu$ on the unit circle satisfies the symmetry $d\\mu(e^{i(2\\pi-\\theta)}) = - d\\mu(e^{i\\theta})$ then the associated OPUC, say $S_n$, are all real. In this case, Delsarte and Genin, in 1986, have shown that the two sequences of para-orthogonal polynomials $\\{zS_{n}(z) + S_{n}^{\\ast}(z)\\}$ and $\\{zS_{n}(z) - S_{n}^{\\ast}(z)\\}$ satisfy three term recurrence formulas and have also explored some further consequences of these sequences of polynomials such as their connections to sequences of orthogonal polynomials on the interval $[-1,1]$. The same authors, in (1988), have"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0719","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"}