3 problems

Let $f$ be a probability density function supported on $[-\frac14,\frac14]$. The norms $\|f\ast f\|_\infty$ and $\|f\ast f\|_2$ are defined using the autoconvolution $f\ast f$. Aut…

Let $f$ be a probability density function supported on $[-\frac14,\frac14]]$. The convolution $f\ast f$ has supremum norm $\|f\ast f\|_\infty$ and $L^2$ norm $\|f\ast f\|_2$. Convo…

Surjectivity conjecture. Every almost surely positive density $g$ on $[0,1]$ is the pdQ transformation of a density function, and hence uniquely represents a location-scale family.