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It is known that, if $f$ is a function holomorphic on a neighbourhood of the closed unit disk, then it belongs to $\\mathcal{H}(b)$, and its norm in $\\mathcal{H}(b)$ can be expressed in terms of the Taylor coefficients of $f$ and $\\phi$ via the formula \\[ \\|f\\|_{\\mathcal{H}(b)}^2=\\sum_{m\\ge0}|\\hat{f}(m)|^2 +\\sum_{m\\ge0}\\Bigl|\\sum_{n\\ge0}\\overline{\\hat{\\phi}(n)}\\hat{f}(m+n)\\Bigr|^2. \\] However, the formula can bre"},"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":"2605.30114","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-28T15:50:08Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"766bf1e57ea20ac049c339702ae7342c99a31c501111bb1229ec7382cbccb410","abstract_canon_sha256":"fe14180c8a2cdbeb084549c62e93d0e6938ae5616e1a56936bf56217d027ba01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:10.146037Z","signature_b64":"N3uSXYGyIdSuPeJogPt5FXkYlr+QJqwc1nx6nRqC828dH/tWpkDwIQZgssBajxVc0HrE2RoKxpppoxFhCWbcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e64525558127061eabdcbc07938626aaa6f025de376d515fdc7f5812f5d19fa5","last_reissued_at":"2026-05-29T02:06:10.145697Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:10.145697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the coefficient formula for de Branges-Rovnyak norms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Thomas Ransford","submitted_at":"2026-05-28T15:50:08Z","abstract_excerpt":"Let $\\mathcal{H}(b)$ be the de Branges-Rovnyak space associated to a non-extreme point $b$ of the unit ball of $H^\\infty$, and let $\\phi=b/a$, where $a$ is the Pythagorean mate of $b$. 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