ABSTRACT
We give in this chapter the heat kernel of the twisted Laplacian Lτ , τ ∈ R\{0}, and the heat kernel of the sub-Laplacian L on the Heisenberg group H1. The following formula is the main tool for the construction of the heat kernel of Lτ for τ ∈ R \ {0}. Theorem 22.1 For all nonnegative integers α, β, µ, and ν,
eα,β ∗1/4 eµ,ν = (2π)1/2δβ,µeα,ν , where δβ,µ is the Kronecker delta given by
δβ,µ =
{ 1, β = µ, 0, β 6= µ.
