{"paper":{"title":"Siciak's homogeneous extremal functions, holomorphic extension and a generalization of Helgason's support theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"J\\\"oran Bergh, Ragnar Sigurdsson","submitted_at":"2019-02-04T11:46:54Z","abstract_excerpt":"We prove that a function, which is defined on a union of lines $\\mathbb{C} E$ through the origin in $\\mathbb{C}^n$ with direction vectors in $E\\subset \\mathbb{C}^n$ and is holomorphic of fixed finite order and finite type along each line, extends to an entire holomorphic function on $\\mathbb{C}^n$ of the same order and finite type, provided that $E$ has positive homogeneous capacity in the sense of Siciak and all directional derivatives along the lines satisfy a necessary compatibility condition at the origin. We are able to estimate the indicator function of the extension in terms of Siciak's"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01134","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"}