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.

中文翻译：

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Schrödinger半群的对角热核估计及其应用

我们建立了对应于一大类对称跳跃过程的无界势的Schrödinger半群的明确而尖锐的对角热核估计。该方法基于双面（狄利克雷）热核估计和对称跳跃过程的固有收缩性的最新发展。结果，我们提出了一个更直接的论据来为相关的非局部算子的特征值产生渐近行为。