Heat Kernels, Smoothness Estimates, and Exponential Decay

Sharp Pointwise Estimates on Heat Kernels

Agmon-Type Exponential Decay Estimates for Pseudodifferential Operators∗

We study generalizations of Agmon-type estimates on eigenfunctions for Schrödinger operators. In the first part, we prove an exponential decay estimate on eigenfunctions for a class of pseudodifferential operators. In the second part, we study the semiclassical limit of ~-pseudodifferential operators, and exponential decay estimates on eigenfunctions and Briet-Combes-Duclos-type resolvent estim...

Sub-gaussian Estimates of Heat Kernels on Infinite Graphs

We prove that a two-sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.

Two-sided estimates of heat kernels on metric measure spaces

3 Some preparatory results 18 3.1 Green operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Harmonic functions and Harnack inequality . . . . . . . . . . . . . . . 22 3.3 Faber-Krahn inequality and mean exit time . . . . . . . . . . . . . . . 24 3.4 Estimates of the exit time . . . . . . . . . . . . . . . . . . . . . . . . . 27 ∗Partially supported by SFB 701 of the Ge...

Characterization of Sharp Global Gaussian Estimates for Schrödinger Heat Kernels

We investigate when the fundamental solution of the Schrödinger equation ∂t = ∆ + V posseses sharp Gaussian bounds global in space and time. We give a characterization for V ≤ 0 and a sufficient condition for general V .