论文标题
近对角线附近的低纤维化热核的小渐近物，nilpotentization及其相关结果
Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results
论文作者
论文摘要
我们建立了小型渐近扩张，用于在对角线附近的低纤维化Hörmander操作员的热核，概括了Métivier和Ben Arous的前一个结果。我们扩展的系数是根据基础次摩nannian结构的nilpotentization确定的。我们的方法纯粹是分析性的，尤其依赖于局部和全球亚小节估计以及热核的小型渐近性局部性质。我们的扩张不仅沿对角线有效，而且在对角线的渐近邻居中有效，这是主要的新颖性，对于为subelliptic laplacians推导了韦尔定律而言，这一事实是有效的。反过来，我们对本身很有趣的低纤维化热核建立了许多其他结果，例如KAC不受边界的原则，渐近算子的偶然扰动，全球平滑性能的渐近扰动，对自降热量半群的全球平滑性能。
We establish small-time asymptotic expansions for heat kernels of hypoelliptic Hörmander operators in a neighborhood of the diagonal, generalizing former results obtained in particular by Métivier and by Ben Arous. The coefficients of our expansions are identified in terms of the nilpotentization of the underlying sub-Riemannian structure. Our approach is purely analytic and relies in particular on local and global subelliptic estimates as well as on the local nature of small-time asymptotics of heat kernels. The fact that our expansions are valid not only along the diagonal but in an asymptotic neighborhood of the diagonal is the main novelty, useful in view of deriving Weyl laws for subelliptic Laplacians. In turn, we establish a number of other results on hypoelliptic heat kernels that are interesting in themselves, such as Kac's principle of not feeling the boundary, asymptotic results for singular perturbations of hypoelliptic operators, global smoothing properties for selfadjoint heat semigroups.
