Heat Trace of non-local operators

TL;DR

This paper generalizes the asymptotic analysis of heat traces from classical Laplacian operators to non-local operators associated with stable and Lévy processes, providing new mathematical insights.

Contribution

It extends van den Berg's two-term asymptotics for heat traces to non-local operators linked to stable and Lévy processes, broadening the scope of spectral analysis.

Findings

Derived two-term asymptotics for non-local operator heat traces

Extended classical results to stable and Lévy process operators

Provided mathematical framework for spectral analysis of non-local operators

Abstract

This paper extends results of M. van den Berg on two-term asymptotics for the trace of Sch\"odinger operators when the Laplacian is replaced by non-local (integral) operators corresponding to rotationally symmetric stable processes and other closely related L\'evy processes.