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Hardy perturbations of subordinated Bessel heat kernels

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arxiv 2409.02853 v1 pith:OWZ7J6DQ submitted 2024-09-04 math.AP math-phmath.FAmath.MPmath.PR

Krzysztof Bogdan , Tomasz Jakubowski , Konstantin Merz This is my paper · ORCID
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keywords besselfunctionshardyheatkernelsperturbationssubordinatedanalysis
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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.

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

    math.AP 2025-06 accept novelty 6.0 of 10

    The heat kernel of the fractional Laplacian with Hardy potential in each angular momentum channel is comparable to the kernel without the potential, multiplied by two known weight factors.

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