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When $g(x)$ and $h(x)$ are given functions, can $f(x)^2+(g*f)(x)+h(x)=0$ be solved for $f(x)$ in closed form (at least with some restrictions to $g,h$)? (The $*$ is not a typo, it really means convolution as in $(f*g)(x)=\int\limits_{\mathbb R}f(y)g(x-y)\,dy$)

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    This is a very interesting question? Have you considered posting bounty on it?2015-01-20

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