Characterization of smooth symbol classes by Gabor matrix decay

Federico Bastianoni, Elena Cordero

For $m\in \mathbb{R}$ we introduce the symbol classes $S^m$, $m\in \mathbb{R}$, consisting of smooth functions $\sigma$ on ${\mathbb{R}}^{2d}$ such that $|\partial^ασ(z)|\leq C_α(1+|z|^2)^{…