Let $f,g$ be smooth and integrable functions from $\mathbb{R}^d$ to $\mathbb{R}$. Can someone help with mentioning some papers that tell me how to find the optimal rigid transformation $O^*$ such that \begin{align*} O^* = \arg\max_{O: O^TO=I} \int_{\mathbb{R}^d} f(O x)g(x)\mathrm{d}x \end{align*} Here I wished the assumptions on $f$ and $g$ to be as few and as weak as possible.
Thanks much!