I've been working with this equation where the unknown factor is the function $f$ that can be complex:
$$1 = f(\vec{x})\int_{\mathbb{R}^3}\ d^3y\ \frac{f(\vec{y})}{|\vec{x} - \vec{y}|^4}$$
Is there any way to solve this equation without using the trial-error method, i.e., without testing different forms for $f$? Anyway, can you see any solution?
Thanks in advance!