If f and g are continuous functions on the right half-line, [0,∞], then f✶g, the convolution of f and g, is defined by(adsbygoogle = window.adsbygoogle || []).push({});

f✶g(x) = ∫_{[0,x]}f(t)g(x-t)dt.

I would like to know if f✶g is a differentiable function of x.

If, for example, g(t) = 1 for t ≥ 0 then f✶g(x) = ∫_{[0,x]}f(t)dt has a derivative equal to f(x). But what about in general?

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# I Differentiability of convolution

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