Solving for $g(y)$ in the following integral equation Given the following integral equation where $f, h$ are known:
$$ f(t) = \int_{t-1}^t{g(y)\cdot h(y)\ \textrm{d}y}$$
Is it possible to solve this for $g(t)$, i.e. get an equation of the form $g(t) = \dots$ (supposing $g, h$ are suitably nice)? I have no idea where to start. I acknowledge that an analytical solution may not even exist in the general case, but I remain hopeful!

If $ g $ and $ h $ are continuous at $ \Bbb R $ , then $ f $ will be differentiable at $ \Bbb R $ and, by chain rule,
$$f'(t)=g(t)h(t)-g(t-1)h(t-1)$$
So,
$$g(t)=g(t-1)\frac{h(t-1)}{h(t)}+\frac{f'(t)}{h(t)}$$
which is a kind of recursive relation.
