{"paper":{"title":"A New Proof Of The Asymptotic Limit Of The $Lp$ Norm Of The Sinc Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"R. Kerman, S. Spektor","submitted_at":"2012-08-19T01:45:15Z","abstract_excerpt":"We improve on the inequality $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq \\frac{1}{\\sqrt p}, {0.2 cm}p\\geq 1,}$ showing that $\\displaystyle{\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt\\leq C(p) \\frac{\\sqrt{3/\\pi}}{\\sqrt p},}$ with $\\displaystyle{\\lim_{p\\longrightarrow \\infty} C(p)=1,}$ and indeed that {align*} \\displaystyle{\\lim_{p\\longrightarrow \\infty}\\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} (\\frac{\\sin^2 t}{t^2})^pdt/ \\frac{\\sqrt{3/\\pi}}{\\sqrt p}=1.} {align*}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3799","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"}