Year: 2025
Type: preprint
Abstract: We construct a nonnegative step function comprising 2,399 equally spaced intervals such that \[ \frac{\|f * f\|_{L^{2}(\mathbb{R})}^{2}}{\|f * f\|_{L^{\infty}(\mathbb{R})}\,\|f * f\|_{L^{1}(\mathbb{R})}} \;\ge\; .926529. \] 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.
Source: arXiv (Cornell University)
Authors: Jaech, Aaron, Joseph, Alan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891870562
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