On Suprema of Autoconvolutions with an Application to Sidon sets

Alexander Cloninger, Stefan Steinerberger

Let $f$ be a nonnegative function supported on $(-1/4,1/4)$. We show $$ \sup_{x \in \mathbb{R}}{\int_{\mathbb{R}}{f(t)f(x-t)dt}} \geq 1.28\left(\int_{-1/4}^{1/4}{f(x)dx} \right)^2…