ABSTRACT
We are interested in solving for u of the initial value problem for the heat equation governed by the sub-Laplacian L, i.e.,{
∂u ∂ρ (z, t, ρ) = −(Lu)(z, t, ρ), u(z, t, 0) = f(z, t)
for all (z, t) ∈ H1 and all time ρ > 0. Formally, u is given by u(z, t, ρ) = (e−ρLf)(z, t), (z, t) ∈ H1, ρ > 0.
