{"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. We prove that \\[ \\int_\\mathbb{R} (M^+ - M^-) |E(x)|^{-2}dx = \\frac{1}{a^2 K(0,0)} \\] where $K$ is the reproducing kernel for $\\mathcal{H}(E)$. 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 $(\\pi a - \\tanh(\\pi a))^{-1} \\pi a$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1157","kind":"arxiv","version":2},"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"}