{"paper":{"title":"Holomorphic functions on subsets of C","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Buma L. Fridman, Daowei Ma","submitted_at":"2010-06-15T22:59:15Z","abstract_excerpt":"Let $\\Gamma $ be a $C^\\infty $ curve in $\\Bbb{C}$ containing 0; it becomes $\\Gamma_\\theta $ after rotation by angle $\\theta $ about 0. Suppose a $C^\\infty $ function $f$ can be extended holomorphically to a neighborhood of each element of the family $\\{\\Gamma_\\theta \\}$. We prove that under some conditions on $\\Gamma $ the function $f$ is necessarily holomorphic in a neighborhood of the origin. In case $\\Gamma $ is a straight segment the well known Bochnak-Siciak Theorem gives such a proof for \\textit{real analyticity}. We also provide several other results related to testing holomorphy proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3105","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"}