Dirichlet Sub-Laplacians on Homogeneous Carnot Groups: Spectral Properties, Asymptotics, and Heat Content

被引：0

作者：

Carfagnini, Marco ^{[1
]}

Gordina, Maria ^{[2
]}

机构：

[1] Univ Calif La Jolla, Dept Math, San Diego, CA 92093 USA

[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2024年 / 2024卷 / 03期

关键词：

SPACES;

D O I：

10.1093/imrn/rnad065

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1894 / 1930

页数：37

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