发表机构
University of Rochester; Queen’s University; University of Trento; University of Virginia（罗切斯特大学; 女王大学; 特伦托大学; 弗吉尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对任意 Carnot 群上次拉普拉斯从属算子，结合多类方法推导其特征值估计、热含量渐近行为等谱性质，完善了相关算子的分析理论。
AI 中文摘要
我们研究任意 Carnot 群上次拉普拉斯从属算子的热含量与谱性质，考虑这类算子在带零 Dirichlet 边界条件的有界开集上的限制并分析其谱特性。针对一大类从属子，我们给出用从属子及次拉普拉斯特征值表示的显式特征值估计，还基于谱间隙给出次拉普拉斯从属算子热含量的长时间渐近行为；对分数阶次拉普拉斯算子，我们证明对应热含量与相对热含量的短时间渐近行为。我们的方法结合了半群方法、概率技术、几何测度论及热核估计。
英文摘要
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.
