{"paper":{"title":"Orthogonal testing families and holomorphic extension from the sphere to the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Luca Baracco, Martino Fassina","submitted_at":"2018-08-22T17:16:29Z","abstract_excerpt":"Let $\\mathbb{B}^2$ denote the open unit ball in $\\mathbb{C}^2$, and let $p\\in \\mathbb{C}^2\\setminus\\overline{\\mathbb{B}^2}$. We prove that if $f$ is an analytic function on the sphere $\\partial\\mathbb{B}^2$ that extends holomorphically in each variable separately and along each complex line through $p$, then $f$ is the trace of a holomorphic function in the ball."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07444","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"}