Schwartz_function
Definition
A function $f \in C^{\infty}\left. \left( \mathbb{R}^{n} \right) \right.$is called a Schwartz function if it goes to zero as $|x| \rightarrow \infty$ faster than any inverse power of $x$, as do all its derivatives. That is, a function is a Schwartz function if there exist real constants $C_{\alpha\beta}$ such that
$$ \sup\limits_{x \in \mathbb{R}^{n}}\left| x^{\alpha}\partial_{\beta}f\left. (x) \right. \right| \leq C^{\alpha\beta} $$where multi-index notation has been used for $\alpha$ and $\beta$.