{"paper":{"title":"Relative Szeg\\H{o} asymptotics for Toeplitz determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Maurice Duits, Rostyslav Kozhan","submitted_at":"2016-11-03T13:59:52Z","abstract_excerpt":"We study the asymptotic behavior, as $n\\to\\infty$, of ratios of Toeplitz determinants $D_n(e^h d\\mu)/D_n(d\\mu)$ defined by a measure $\\mu$ on the unit circle and a sufficiently smooth function $h$. The approach we follow is based on the theory of orthogonal polynomials. We prove that the second order asymptotics depends on $h$ and only a few Verblunsky coefficients associated to $\\mu$. As a result, we establish a relative version of the Strong Szeg\\H{o} Limit Theorem for a wide class of measures $\\mu$ with essential support on a single arc. In particular, this allows the measure to have a sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01020","kind":"arxiv","version":3},"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"}