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As an application we determine the optimal majorant and minorant for the Heaviside function that vanish at a fixed point $\\alpha = ia$ on the imaginary axis. We show that the difference of majorant and minorant has integral value $(\\pi a - \\tanh(\\pi a))^{-1} \\pi a$."},"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":"1311.1157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-05T18:50:41Z","cross_cats_sorted":[],"title_canon_sha256":"a3a3493e5ee46f623e773157a36c178b62fa3e3e0934635d80fb25422201f38e","abstract_canon_sha256":"69faafb903f7cfee37c656dd00044ad006ca6c6b0364f30f2f45922d4ede50d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:29.264353Z","signature_b64":"4oO2n3qenFBlMt7NMjCjceQSWUW/mi5qiyAYsrRKmx/avZnah5171u/z87w0cg0vyIXRGt+P76IiJtGdh+O7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9a11bd8095748a7a905a5b083b8cecb2df48e943e2800b592153d7b2e8f7580","last_reissued_at":"2026-05-18T01:08:29.263771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:29.263771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal functions with vanishing condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Friedrich Littmann, Mark Spanier","submitted_at":"2013-11-05T18:50:41Z","abstract_excerpt":"We determine the optimal majorant $M^+$ and minorant $M^-$ of exponential type for the truncation of $x\\mapsto (x^2+a^2)^{-1}$ with respect to general de Branges measures. 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