Integral Transform Wanted

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

flag	asked Apr 24 2011 at 5:50 Yrogirg 163●5

	The integral $f(\mathbf{r}_1,\mathbf{r}_2)$ depends on $\|\mathbf{r}_1-\mathbf{r}_2\|$ only. To go further, it might help to specify the function $g$ somewhat. – Didier Piau Apr 24 2011 at 9:08
	>To go further, it might help to specify the function g somewhat. Unfortunately this integral is the part of an equation for g. Indeed there is a lot of integrals of the same structure in that equation. g itself is a radial distribution function encountered in statistical mechanics, but that fact is really not very much to give. – Yrogirg Apr 24 2011 at 17:09