Trace estimates for unimodal L\'evy processes

TL;DR

This paper provides a precise two-term approximation for the trace of the Dirichlet heat kernel at small times for bounded smooth domains influenced by unimodal Lévy processes under weak scaling conditions.

Contribution

It introduces a novel two-term small-time approximation for the heat kernel trace specific to unimodal Lévy processes with weak scaling, extending existing results.

Findings

Two-term small-time approximation derived

Applicable to bounded smooth domains

Enhances understanding of Lévy process heat kernels

Abstract

We give two-term small-time approximation for the trace of the Dirichlet heat kernel of bounded smooth domain for unimodal L\'evy processes satisfying the weak scaling conditions.