发表机构
University of Gothenburg; Chalmers University of Technology（哥德堡大学; 查尔姆斯理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明 Lipschitz 域上 Dirichlet Laplacian 加权热迹的渐近展开，并应用于加权 Riesz 均值和特征函数局部化测度的收敛。
AI 中文摘要
我们证明了有界 Lipschitz 域上 Dirichlet Laplacian 的加权热迹的渐近展开。权重由到边界距离的幂次乘以一个在边界附近连续的有界函数给出。根据权重的指数，我们得到一项或两项渐近式。我们给出两个应用，即任意阶加权 Riesz 均值的一项渐近式版本，以及描述 Laplace 特征函数局部化的一族测度的收敛结果。
英文摘要
We prove an asymptotic expansion of a weighted heat trace of the Dirichlet Laplacian on a bounded Lipschitz domain. The weight is given by a power of the distance to the boundary times a bounded function that is continuous near the boundary. Depending on the exponent of the weight, we obtain one-term or two-term asymptotics. We present two applications, namely a version of one-term asymptotics of weighted Riesz means for arbitrary orders, as well as convergence results for a family of measures that describes localization of Laplace eigenfunctions.
