1 results
An optimal
$L^2$ autoconvolution inequality
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 1 / March 2024
- Published online by Cambridge University Press:
- 05 July 2023, pp. 108-121
- Print publication:
- March 2024
-
- Article
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Let
$\mathcal {F}$ denote the set of functions 
$f \colon [-1/2,1/2] \to \mathbb {R}_{\geq 0}$ such that 
$\int f = 1$. We determine the value of 
$\inf _{f \in \mathcal {F}} \| f \ast f \|_2^2$ up to a 
$4 \cdot 10^{-6}$ 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 
$(g,h) \in \{ (2,2),(3,2),(4,2),(1,3),(1,4)\}$.
