{"paper":{"title":"Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Alfredo Dea\\~no","submitted_at":"2014-02-10T10:13:20Z","abstract_excerpt":"We consider polynomials $p_n^{\\omega}(x)$ that are orthogonal with respect to the oscillatory weight $w(x)=e^{i\\omega x}$ on $[-1,1]$, where $\\omega>0$ is a real parameter. A first analysis of $p_n^{\\omega}(x)$ for large values of $\\omega$ was carried out in connection with complex Gaussian quadrature rules with uniform good properties in $\\omega$. In this contribution we study the existence, asymptotic behavior and asymptotic distribution of the roots of $p_n^{\\omega}(x)$ in the complex plane as $n\\to\\infty$. The parameter $\\omega$ grows with $n$ linearly. The tools used are logarithmic poten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2085","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"}