标题： 对自卷积不等式下界的进一步改进 显示英文标题

标题： Further Improvements to the Lower Bound for an Autoconvolution Inequality

摘要： 我们构建一个由2,399个等距间隔组成的非负阶梯函数，使得\[ \frac{\|f * f\|_{L^{2}(\mathbb{R})}^{2}}{\|f * f\|_{L^{\infty}(\mathbb{R})}\,\|f * f\|_{L^{1}(\mathbb{R})}} \;\ge\; .926529. \]。通过对这个559间隔优化器使用4倍上采样过程，我们进一步将界限提高到$.94136$，关闭了之前最佳界限（575间隔时的.901562）和1的平凡上限之间大约40%的差距。 显示英文摘要

摘要： 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.