Hardy perturbations of subordinated Bessel heat kernels

TL;DR

This paper establishes precise bounds for the transition densities of Hardy-perturbed subordinated Bessel heat kernels, advancing understanding in spectral theory related to relativistic atoms.

Contribution

It provides the first matching upper and lower bounds for these perturbed heat kernels using supermedian and invariant functions.

Findings

Established tight bounds for Hardy-perturbed Bessel heat kernels

Utilized supermedian functions for analysis

Enhanced spectral theory understanding in relativistic quantum models

Abstract

Motivated by the spectral theory of relativistic atoms, we prove matching upper and lower bounds for the transition density of Hardy perturbations of subordinated Bessel heat kernels. The analysis is based on suitable supermedian functions, in particular invariant functions.