Preprint

Inserted: 3 sep 2026
Last Updated: 3 sep 2026

Year: 2026

Abstract:

We study heat content and spectral properties of subordinated sub-Laplacians on arbitrary Carnot groups. We consider restrictions of such operators to bounded open sets with zero Dirichlet boundary condition and study their spectral properties. In particular, for a large class of subordinators we give explicit eigenvalue estimates in terms of the subordinator and the eigenvalues of the sub-Laplacian. We also provide large-time asymptotics of the heat content for the subordinated sub-Laplacian in terms of its spectral gap. For fractional sub-Laplacians we prove short-time asymptotics for the corresponding heat content and relative heat content. Our approach combines semigroup methods, probabilistic techniques, geometric measure theory, and heat kernel estimates.

Download:

• Subordination_Heisenberg-7.pdf