{"paper":{"title":"Simultaneous approximation and interpolation of functions on continua in the complex plane","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"I. E. Pritsker, R. S. Varga, V. V. Andrievskii","submitted_at":"2000-05-03T15:58:22Z","abstract_excerpt":"We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, $k \\ge 1$) for analytic functions defined on a continuum E in the complex plane, which simultaneously interpolate at given points of E. Furthermore, the error in this approximation is decaying as $e^{-cn^\\alpha}$ strictly inside E, where c and $\\alpha$ are positive constants independent of the degree n of the approximating polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0005032","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"}