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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.02910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-13T08:22:31Z","cross_cats_sorted":[],"title_canon_sha256":"8efc57a8de34e04ed2a4dfc397fe9c7ee47d6120de125455f2aead0da06c221a","abstract_canon_sha256":"ba4b67a6dfc30e8917ae6132d09454cb833ffe44a1525d2e350eec82d9ad7be9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:30.939526Z","signature_b64":"9qAf/iDG8Eg6rAf7ya67mnVRmMjZGjcu10/AbzxhmMHqMIZkIFHNEUnIQnwE/pRdxW+VlQmHVnEvQbES49lqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"726931ad33c8c0a77c53465752b2d5bbb9d99735360a9a12a082bf27b384726b","last_reissued_at":"2026-05-18T02:29:30.938983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:30.938983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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