  The purpose of this article is to establish upper and lower estimates for the
integral kernel of the semigroup exp(-tP) associated to a classical, strongly
elliptic pseudodifferential operator P of positive order on a closed manifold.
The Poissonian bounds generalize those obtained for perturbations of fractional
powers of the Laplacian. In the selfadjoint case, extensions to t in C_+ are
studied. In particular, our results apply to the Dirichlet-to-Neumann
semigroup.
