For any non-negative integer $n$ I have the following: $$\int_0^\infty x^n f(x)dx=\int_0^\infty \sum_{k=0}^na_{kn}x^kg(x)dx$$
So, I can write the system of equations (when $n=0,1,2.\ldots$).
I know the coefficients $a_{kn}$ and $g(x)$.
Is it possible to find exactly or approximately the function $f(x)$?
Thank you.