Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators

Abstract

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.

31 pages, to appear in J. Evolution Eq

References in corpus (2)

• Heat kernel estimates for critical fractional diffusion operator
• Analysis of the heat kernel of the Dirichlet-to-Neumann operator

Cited by in corpus (1)

• One can hear the area and curvature of boundary of a domain by hearing the Steklov eigenvalues