{"paper":{"title":"Analytic scattering theory for Jacobi operators and Bernstein-Szeg\\\"o asymptotics of orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.CA","authors_text":"D. R. Yafaev","submitted_at":"2017-11-14T09:51:49Z","abstract_excerpt":"We study semi-infinite Jacobi matrices $H=H_{0}+V$ corresponding to trace class perturbations $V$ of the \"free\" discrete Schr\\\"odinger operator $H_{0}$. Our goal is to construct various spectral quantities of the operator $H$, such as the weight function, eigenfunctions of its continuous spectrum, the wave operators for the pair $H_{0}$, $H$, the scattering matrix, the spectral shift function, etc.\n  This allows us to find the asymptotic behavior of the orthonormal polynomials $P_{n}(z)$ associated to the Jacobi matrix $H $ as $n\\to\\infty$. In particular, we consider the case of $z$ inside the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05029","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"}