Hardy perturbations of subordinated Bessel heat kernels

2024/09/04 by Krzysztof Bogdan, Bogdan, Krzysztof, Tomasz Jakubowski +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2409.02853

openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels

Related

• Subordinated Bessel heat kernels
• Fourier-Bessel heat kernel estimates
• Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels
• Asymptotic behaviour of the Bessel heat kernels
• Relativistic stable operators with critical potentials