On-diagonal Heat Kernel Estimates for Schrödinger Semigroups and Their Application

Abstract

We establish explicit and sharp on-diagonal heat kernel estimates for Schrödinger semigroups with unbounded potentials corresponding to a large class of symmetric jump processes. The approach is based on recent developments on the two-sided (Dirichlet) heat kernel estimates and intrinsic contractivity properties for symmetric jump processes. As a consequence, we present a more direct argument to yield asymptotic behaviors for eigenvalues of associated nonlocal operators.

Keywords

Schrödinger semigroup / (Dirichlet) heat kernel / Intrinsic contractivity property / Eigenvalue