{"paper":{"title":"Approximating z-bar in the Bergman space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dmitry Khavinson, Matthew Fleeman","submitted_at":"2015-09-04T08:48:54Z","abstract_excerpt":"We consider the problem of finding the best approximation to $\\bar{z}$ in the Bergman Space $A^{2}(\\Omega)$. We show that this best approximation is the derivative of the solution to the Dirichlet problem on $\\partial\\Omega$ with data $\\left|z\\right|^{2}$ and give examples of domains where the best approximation is a polynomial, or a rational function. Finally, we obtain the \"isoperimetric sandwich\" for $dist(\\overline{z},\\Omega)$ that yields the celebrated St. Venant inequality for torsional rigidity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01370","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"}