1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) 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∈C+ are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup.
Journal of Evolution Equations, 2014, Vol 14, p. 49-83