{"paper":{"title":"Some properties of Faber-Walsh polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CV","authors_text":"Olivier S\\`ete","submitted_at":"2013-06-06T09:14:30Z","abstract_excerpt":"Walsh introduced a generalisation of Faber polynomials to certain compact sets which need not be connected. We derive several equivalent representations of these Faber-Walsh polynomials, analogous to representations of Faber polynomials. Some simple asymptotic properties of the Faber-Walsh polynomials on the complement of the compact set are established. We further show that suitably normalised Faber-Walsh polynomials are asymptotically optimal polynomials in the sense of [Eiermann and Niethammer 1983]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1347","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"}