Hello! Imagine I have a function

$f(r_1, r_2) = \int_{-\infty}^\infty g(|r_1 - r_3|) g(|r_1 - r_4|) g(|r_2 - r_3|) g(|r_2 - r_4|) g(|r_3 - r_4|) \; d r_3 d r_4$

Is there a way I could get rid of the integration via some (integral) transform?

so transformed $f$, that is $\hat f (k_1, k_2)$, was some algebraic combination of $\hat g (k_1, k_2)$?

Actually I need a bit more complicated case of $r$ being 3D vectrors, but I think the solution for a scalar version should be just the same

$f(\boldsymbol r_1, \boldsymbol r_2) = \int g(|\boldsymbol r_1 - \boldsymbol r_3|) g(|\boldsymbol r_1 - \boldsymbol r_4|) g(|\boldsymbol r_2 - \boldsymbol r_3|) g(|\boldsymbol r_2 - \boldsymbol r_4|) g(|\boldsymbol r_3 - \boldsymbol r_4|) \; d \boldsymbol r_3 d \boldsymbol r_4$