Let's say I have an equation of form:
$\int_{-\infty}^\infty dy f(x,y) g(y,z) = h(x,z)$
where I've been given $g$ and $h$, and need to find $f$. I shouldn't in general expect a suitable $f$ to exist, or for it to be unique if it does. But does there exist a general process, or some sort of approach, for attempting to find a solution? I have a certain $g$ and $h$ in mind, but I would like to understand how to approach this problem more generally.
