Fix any $f\in\mathcal{S}_x(\mathbb{R}^d\to\mathbb{C})$, i.e. $f$ is a Schwartz function from $\mathbb{R}^d$ to $\mathbb{C}$. Is it always possible to find $g,h\in\mathcal{S}_x(\mathbb{R}^d\to\mathbb{C})$ such that $f(x)=g(x)h(x)$ for all $x\in\mathbb{R}^d$?
The square root seems a good choice, but I find this problem. So I am not sure what I am supposed to do to solve or disprove this problem.
Thank you!