{"paper":{"title":"Constructive approximation in de Branges-Rovnyak spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"E. Fricain, J. Mashreghi, K. Kellay (IMB), O. El-Fallah, Ransford Tom","submitted_at":"2015-01-13T08:22:31Z","abstract_excerpt":"In most classical holomorphic function spaces on the unit disk, a function $f$ can be approximated in the norm of the space by its dilates $f\\_r(z):=f(rz)~(r \\textless{} 1)$.\nWe show that this is \\emph{not} the case for the de Branges--Rovnyak spaces $\\cH(b)$. More precisely, we give an example of a non-extreme point $b$ of the unit ball of $H^\\infty$ and a function $f\\in\\cH(b)$ such that $\\lim\\_{r\\to1^-}\\|f\\_r\\|\\_{\\cH(b)}=\\infty$.\nIt is  known that, if $b$ is a non-extreme point of the unit ball of $H^\\infty$, then polynomials are dense in $\\cH(b)$. We give the first constructive proof of thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02910","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"}