I'm trying to find the construction of the heat semigroup in Heisenberg groups, but I haven't found anything. In particular, I'm trying to find out if the semigroup in the Heisenberg group has the properties of being of class $C_0$ and analytic, to find out if some results from Regularity of Mild Solutions for Analytic Semigroups are valid as
This result is from PAZY's book and provides regularity for the problem $u_t - Au(t) = f(t)$. Are there similar results for the heat semigroup in Heisenberg groups (or in Lie groups in general)? Can you recommend me some book/article? Thanks in advance.