Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth

Alessio Martini, Fulvio Ricci, Leonardo Tolomeo

Let $\mathcal{L}$ be a sub-Laplacian on a connected Lie group $G$ of polynomial growth. It is well known that, if $F:\mathbb{R}\to \mathbb{C}$ is in the Schwartz class $\mathcal…