Further Improvements to the Lower Bound for an Autoconvolution Inequality

2025/08/04 by Jaech, Aaron, Joseph, Alan · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.02803

Abstract

We construct a nonnegative step function comprising 2,399 equally spaced intervals such that \frac‖f * f‖_L²(ℝ)²‖f * f‖_L^∞(ℝ) ‖f * f‖_L¹(ℝ) ≥ .926529. Using a 4x upsampling procedure on this 559-interval optimizer, we further increase the bound to .94136, closing roughly 40% of the gap between the previous best bound (.901562 on 575 intervals) and the trivial upper limit of 1.

Citations

• An improved example for an autoconvolution inequality
• Improved bounds on the supremum of autoconvolutions

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• ThetaEvolve: Test-time Learning on Open Problems

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