Let $n \in \mathbb N$, let $m \in \mathbb R$, and let $a \in S^m_{1,0}(\mathbb R^n_x \times \mathbb R^n_\xi)$ be a complex-valued scalar symbol. Define the Kohn-Nirenberg operator
such that ${}^tA - \operatorname{Op}({}^ta)$ has a smoothing Schwartz kernel, and ${}^ta$ is determined modulo $S^{-\infty}$ by the asymptotic expansion