An almost-tight L² autoconvolution inequality

2022/10/28 by Ethan Patrick White, White, Ethan Patrick · 1 citation
Engineering · Mathematics · #05A08 #11B13 #42A05 #90C25 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2210.16437

openalex publication_date 2022/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F denote the set of functions f \colon [-1/2,1/2] → ℝ such that ∫ f = 1. We determine the value of inf_{f ∈ F} ‖ f ∗ f ‖₂ up to a 0.0014% error, thereby making progress on a problem asked by Ben Green. Furthermore, we prove that a unique minimizer exists. As a corollary, we obtain improvements on the maximum size of B_h[g] sets for (g,h) ∈ \ (2,2),(3,2),(4,2),(1,3),(1,4)\.

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