{"paper":{"title":"Bohr's phenomenon on a regular condensator in the complex plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Emmanuel Mazzilli, Patrice Lass\\`ere","submitted_at":"2010-08-25T06:56:41Z","abstract_excerpt":"We prove the following generalisation of Bohr theorem : let $K\\subset\\mathbb C$ a continuum, $(F_n)_n$ its Faber polynomials, $\\Omega_R=\\{\\Phi_K<R\\}, (R>1)$ the levels sets of the Green function; then there exists $R_0>1$ such that for any $f=\\sum_n a_n F_n\\in\\mathscr O(\\Omega_{R_0})$ : $f(\\Omega_{R_0})\\subset D(0,1)$ implies $\\sum_n|a_n|\\cdot|F_n|_K<1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4215","kind":"arxiv","version":4},"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"}