{"paper":{"title":"Perturbation of orthogonal polynomials on an arc of the unit circle","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Leonid B. Golinskii, Paul G. Nevai, Walter Van Assche","submitted_at":"1995-10-08T00:00:00Z","abstract_excerpt":"Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szeg\\H{o} recurrences. We assume that the reflection coefficients converge to some complex number a with 0 < |a| < 1. The polynomials then live essentially on the arc {e^(i theta): alpha <= theta <= 2 pi - alpha} where cos alpha/2 = sqrt(1-|a|^2) with 0 <= alpha <= 2 pi. We analyze the orthogonal polynomials by comparing them with the orthogonal polynomials with constant reflection coefficients, which were studied earlier by Ya. L. Geronimus and N. I. Akhiezer. In particular, we sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9510211","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"}