Analysis of the heat kernel of the Dirichlet-to-Neumann operator

We prove Poisson upper bounds for the kernel (Kt)t>0(Kt)t>0 of the semigroup generated by the Dirichlet-to-Neumann operator if the underlying domain is bounded and has a C∞C∞-boundary. We also prove Poisson bounds for KzKz for all z in the right half-plane and for all its derivatives.