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We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and study their spectral properties. We prove that these operators have a pure point spectrum and prove the… Click to show full abstract
We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and study their spectral properties. We prove that these operators have a pure point spectrum and prove the existence of the spectral gap. In addition, we give applications to the small ball problem for a hypoelliptic Brownian motion and the large time behavior of the heat content in a regular domain.
Keywords:
sub laplacians;
homogeneous carnot;
dirichlet sub;
heat content;
spectral properties
Journal Title: International Mathematics Research Notices
Year Published: 2022
Link to full text (if available)
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Journal Title: International Mathematics Research Notices
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!