On integral estimates of non-negative positive definite functions

Andrey Efimov, Marcell Gaal, Szilard Gy. Revesz

Let $\ell >0$ be arbitrary. We introduce the extremal quantities $$ G(\ell):=\frac{\sup_{f} \int_{-\ell}^{\ell} f\,dx}{\int_{-1}^1 f\,dx},\quad C(\ell):=\frac{\sup_{f} \sup_{a\in {\…