Abstract
The purpose of this article is to establish upper and lower estimates for the integral kernel of the semigroup exp(−t P) associated with 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 \({t \in{\mathbb C}_+}\) are studied. In particular, our results apply to the Dirichlet-to-Neumann semigroup.
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Heiko Gimperlein was partially supported by the Danish Science Foundation (FNU) through research Grant 10-082866 and the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92).
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Gimperlein, H., Grubb, G. Heat kernel estimates for pseudodifferential operators, fractional Laplacians and Dirichlet-to-Neumann operators. J. Evol. Equ. 14, 49–83 (2014). https://doi.org/10.1007/s00028-013-0206-2
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DOI: https://doi.org/10.1007/s00028-013-0206-2