次椭圆Laplace算子特征值的迹公式

Trace Formula of Eigenvalues of Subelliptic Laplacian

考虑Heisenberg群上次椭圆算子特征值的Riesz平均,先建立相关特征值的迹公式,得到对应的Riesz平均,再借助Riesz平均,研究Heisenberg群上次椭圆算子的离散谱,建立该算子特征值的Riesz平均不等式,进而估计其特征值.

The authors mainly focused their attention on the Riesz means of the eigenvalues of subelliptic Laplacian on the Heisenberg group, established the trace formula of associated eigenvalues, then obtained the corresponding Riesz means. We can use the Riesz means to study discrete spectrum of subelliptic Laplaeian on the Heisenberg group, to establish inequalitiy for Riesz means of the eigenvalues of operators and to estimate eigenvalues.