{"paper":{"title":"From local to global asymptotic behaviour of orthogonal polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Artur Nicolau, Roman Bessonov","submitted_at":"2026-06-03T09:09:52Z","abstract_excerpt":"Let $\\{\\phi^*_n\\}$ be the sequence of reflected orthogonal polynomials on the unit circle $\\partial \\mathbb{D}$ generated by a measure $\\mu$ of Szeg\\H{o} class, and let $D_{\\mu}$ be the Szeg\\H{o} function of $\\mu$. We prove the uniform Ces\\`aro asymptotics $$ \\sup_{z \\in \\Gamma_\\zeta}\\Biggl(\\frac{1}{n}\\sum_{k = 0}^{n-1}\\Bigl||\\phi_k^*(z) D_{\\mu}(z)|^2 - 1\\Bigr|\\Biggr) \\to 0, \\qquad n \\to \\infty, $$ for almost all Stolz angles $\\Gamma_{\\zeta}$, $\\zeta\\in \\partial \\mathbb{D}$. This extends a well-known asymptotic result of M\\'at\\'e, Nevai, and Totik (1991) from the local scale $O(1/n)$ near $\\pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04640","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04640/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}