Is the answer to the following question positive? The convolution of two $L^2(\mathbb R)$ functions is continuous
I briefly recall it here: Take $f$ and $g$ $\in L^2(\mathbb R)$, then I want to show that $\lim_{h \to 0} \int_\mathbb{R} f(x-y-h)g(y)dy = f \ast g(x)$.
The question has an answer but it has not been accepted yet.