{"paper":{"title":"On the convergence on nonlinear Pad\\'e--Chebyshev approximations to the multivalued analytic functions, variation of equilibrium energy and $S$-property of stationary compacts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrei A. Gonchar, Evguenii A. Rakhmanov, Sergey P. Suetin","submitted_at":"2010-12-01T12:02:49Z","abstract_excerpt":"Some new results on the convergence of nonlinear diagonal Pad\\'e--Chebyshev approximations to multivalued analytic function given on the segment $[-1,1]$, are proved. We show that these approximations converge to the given function in the \"maxmimal\" domain of its meromorphity and that the boundary of this maxmimal domain is an $S$-curve.\n  The results of the work have been announced in abs/1009.4813\n  Bibliography: 57 items."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0170","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"}