Let $\Gamma$ be a smooth closed curve. Suppose $f\in L^2(\Gamma,ds)$ and $g$ is defined everywhere on $\mathbb{C}$ with compact support. Moreover $\frac{dg}{dz}$ exists everywhere but point $z=0$. Then can we conclude $f{*}g=\int_\Gamma f(w)g(w-z)ds(w)$ is differentiable?
2026-03-25 23:17:58.1774480678
Differentiabilty of certain convolution
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