{"paper":{"title":"Szeg\\H{o}-type asymptotics for ray sequences of Frobenius-Pad\\'e approximants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander I. Aptekarev, Alexey I. Bogolubsky, Maxim L. Yattselev","submitted_at":"2016-05-31T15:26:48Z","abstract_excerpt":"Let $\\widehat\\sigma$ be a Cauchy transform of a possibly complex-valued Borel measure $\\sigma$ and $\\{p_n\\}$ be a system of orthonormal polynomials with respect to a measure $\\mu$, $\\mathrm{supp}(\\mu)\\cap\\mathrm{supp}(\\sigma)=\\varnothing$. An $(m,n)$-th Frobenius-Pad\\'e approximant to $\\widehat\\sigma$ is a rational function $P/Q$, $\\mathrm{deg}(P)\\leq m$, $\\mathrm{deg}(Q)\\leq n$, such that the first $m+n+1$ Fourier coefficients of the linear form $Q\\widehat\\sigma-P$ vanish when the form is developed into a series with respect to the polynomials $p_n$. We investigate the convergence of the Frob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09672","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"}