{"paper":{"title":"A note on a conjecture concerning boundary uniqueness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Abtin Daghighi, Steven G. Krantz","submitted_at":"2014-07-07T16:32:07Z","abstract_excerpt":"We consider the following conjecture (from Huang, et al): Let $\\Delta^+$ denote the upper half disc in $\\mathbb{C}$ and let $\\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\\mathbb{C}$). Assume that $F$ is a holomorphic function on $\\Delta^+$ with continuous extension up to $\\gamma$ such that $F$ maps $\\gamma$ into $\\{|\\mbox{Im} z|\\leq C|\\mbox{Re} z|\\},$ for some positive $C.$ If $F$ vanishes to infinite order at $0$ then $F$ vanishes identically. We show that given the conditions of the conjecture, either $F\\equiv 0$ or there is a sequence in $\\Delta^+$, converging to $0,$ alo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1763","kind":"arxiv","version":2},"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"}