{"paper":{"title":"Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Martinez-Finkelshtein, A. Sri Ranga, Daniel O. Veronese","submitted_at":"2015-05-28T18:24:02Z","abstract_excerpt":"Given a non-trivial Borel measure $\\mu$ on the unit circle $\\mathbb T$, the corresponding reproducing (or Christoffel-Darboux) kernels with one of the variables fixed at $z=1$ constitute a family of so-called para-orthogonal polynomials, whose zeros belong to $\\mathbb T$. With a proper normalization they satisfy a three-term recurrence relation determined by two sequence of real coefficients, $\\{c_n\\}$ and $\\{d_n\\}$, where $\\{d_n\\}$ is additionally a positive chain sequence. Coefficients $(c_n,d_n)$ provide a parametrization of a family of measures related to $\\mu$ by addition of a mass point "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07788","kind":"arxiv","version":2},"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"}