{"paper":{"title":"Traces of analytic uniform algebras on subvarieties and test collections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.CV","authors_text":"Daniel Est\\'evez, Dmitry Yakubovich, Michael A. Dritschel","submitted_at":"2015-05-07T08:32:35Z","abstract_excerpt":"Given a complex domain $\\Omega$ and analytic functions $\\varphi_1,\\ldots,\\varphi_n : \\Omega \\to \\mathbb{D}$, we give geometric conditions for $H^\\infty(\\Omega)$ to be generated by functions of the form $g \\circ \\varphi_k$, $g \\in H^\\infty(\\mathbb{D})$. We apply these results to the extension of bounded functions on an analytic one-dimensional complex subvariety of the polydisk $\\mathbb{D}^n$ to functions in the Schur-Agler algebra of $\\mathbb{D}^n$, with an estimate on the norm of the extension. Our proofs use some extension of the techniques of separation of singularities by Havin, Nersessian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01838","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"}