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Heat content and spectrum for subordinated sub-Laplacians

  • Maria Gordina
  • Liangbing Luo
  • Andrea Pinamonti
  • Rohan Sarkar
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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.

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Cite

BibTeXRIS
BibTeX
@misc{gordina2026heat,
  title = {{Heat content and spectrum for subordinated sub-Laplacians}},
  author = {Maria Gordina and Liangbing Luo and Andrea Pinamonti and Rohan Sarkar},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04045},
  eprint = {2609.04045},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04045},
}
RIS
TY  - UNPB
TI  - Heat content and spectrum for subordinated sub-Laplacians
AU  - Maria Gordina
AU  - Liangbing Luo
AU  - Andrea Pinamonti
AU  - Rohan Sarkar
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04045
UR  - https://arxiv.org/abs/2609.04045
AB  - 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.
ER  -