论文标题
均质Carnot群体的Dirichlet子拉普拉斯人：光谱特性，渐近性和热含量
Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content
论文作者
论文摘要
我们考虑在同质Carnot组中的开放式集合中的次蓝晶片，并研究其光谱特性。我们证明这些运算符具有纯点光谱，并证明了光谱间隙的存在。此外，我们将适用于小球问题，以进行低纤维化的布朗运动和常规域中的热含量的较大时间行为。
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.
