Relativistic stable operators with critical potentials

TL;DR

This paper provides precise two-sided estimates for the heat kernel of a relativistic stable operator when influenced by a critical Hardy potential, advancing understanding of such operators in mathematical physics.

Contribution

It introduces sharp local in time estimates for the heat kernel of relativistic stable operators with critical potentials, a novel analysis in this context.

Findings

Established sharp two-sided heat kernel estimates

Analyzed the impact of critical Hardy potentials

Enhanced understanding of relativistic stable operators

Abstract

We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.