论文标题
几乎紧密的$ l^2 $自动卷积不平等
An almost-tight $L^2$ autoconvolution inequality
论文作者
论文摘要
令$ \ mathcal {f} $表示函数集$ f \ colon [-1/2,1/2] \ to \ mathbb {r} $，这样$ \ int f = 1 $。我们确定$ \ inf_ {f \ in \ mathcal {f}} \ |的值f \ ast f \ | _2 $最高为0.0014 \％错误，从而在Ben Green问的问题上取得了进展。此外，我们证明存在独特的最小化器。作为推论，我们获得了$（g，h）\ in \ in \ {（2,2），（3,2），（4,2），（4,2），（1,3），（1,4）$的最大大小[g] $集的最大大小。
Let $\mathcal{F}$ denote the set of functions $f \colon [-1/2,1/2] \to \mathbb{R}$ such that $\int f = 1$. We determine the value of $\inf_{f \in \mathcal{F}} \| f \ast f \|_2$ 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 $(g,h) \in \{ (2,2),(3,2),(4,2),(1,3),(1,4)\}$.
