A New Proof Of The Asymptotic Limit Of The Lp Norm Of The Sinc Function

2012/08/19 by Ron Kerman, R. Kerman, Susanna Spektor +3
Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Mathematics and Applications #math.CA #math.FA

paper · pdf · doi:10.48550/arxiv.1208.3799

3 pages

arxiv created 2012/08/19 · openalex publication_date 2012/08/19 · arxiv updated 2012/08/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We improve on the inequality \frac1π∫_-∞^∞ ((sin² t)/(t²))^pdt≤ (1)/(√ p), 0.2 cmp≥ 1, showing that \frac1π∫_-∞^∞ ((sin² t)/(t²))^pdt≤ C(p) (√(3/π))/(√ p), with lim_{p\longrightarrow ∞} C(p)=1, and indeed that align* lim_{p\longrightarrow ∞}\frac1π∫_-∞^∞ ((sin² t)/(t²))^pdt/ (√(3/π))/(√ p)=1. align*

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