{"paper":{"title":"Jost Functions and Jost Solutions for Jacobi Matrices, I. A Necessary and Sufficient Condition for Szego Asymptotics","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.SP","authors_text":"Barry Simon (Caltech), David Damanik (Caltech)","submitted_at":"2005-02-23T18:00:51Z","abstract_excerpt":"We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szeg\\H{o} asymptotics off the real axis. A key idea is to prove the equivalence of Szeg\\H{o} asymptotics and of Jost asymptotics for the Jost solution. We also prove $L^2$ convergence of Szeg\\H{o} asymptotics on the spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502486","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"}