{"paper":{"title":"On distributional point values and boundary values of analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Jasson Vindas, Ricardo Estrada","submitted_at":"2013-03-11T11:56:42Z","abstract_excerpt":"We give the following version of Fatou's theorem for distributions that are boundary values of analytic functions. We prove that if $f\\in\\mathcal{D}^{\\prime}(a,b) $ is the distributional limit of the analytic function $F$ defined in a region of the form $(a,b) \\times(0,R),$ if the one sided distributional limit exists, $f(x_{0}+0) =\\gamma,$ and if $f$ is distributionally bounded at $x=x_{0}$, then the \\L ojasiewicz point value exists, $f(x_{0})=\\gamma$ distributionally, and in particular $F(z)\\to \\gamma$ as $z\\to x_{0}$ in a non-tangential fashion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2494","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"}