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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.

carlos85
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  • Yes https://math.stackexchange.com/questions/2915085/the-convolution-of-two-l2-mathbb-r-functions-is-continuous?noredirect=1&lq=1 – Christophe Leuridan May 24 '22 at 11:32
  • The answer there is correct and it has been upvoted many times. Some askers don't care to approve answers and the questions remain in the unanswered list – Kavi Rama Murthy May 24 '22 at 11:34

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