次椭圆Laplace算子特征值的迹公式

J4 ›› 2010, Vol. 48 ›› Issue (06): 899-902.

次椭圆Laplace算子特征值的迹公式

贾高, 熊雅

上海理工大学理学院, 上海 200090

收稿日期:2010-03-24 出版日期:2010-11-26 发布日期:2010-11-26
通讯作者: 贾高 E-mail:gaojia@usst.edu.cn

Trace Formula of Eigenvalues of Subelliptic Laplacian

JIA Gao, XIONG Ya

College of Science, University of Shanghai for Science and Technology, Shanghai 200090, China

Received:2010-03-24 Online:2010-11-26 Published:2010-11-26
Contact: JIA Gao E-mail:gaojia@usst.edu.cn

摘要/Abstract

摘要：

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.

关键词: Heisenberg群, Riesz平均, Lie括号, 次椭圆Laplace算子

Abstract:

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 Laplacian on the Heisenberg group, to establish inequalitiy for Riesz means of the eigenvalues of operators and to estimate eigenvalues.

Key words: Heisenberg group, Riesz means, Lie bracket, subelliptic Laplacian

中图分类号:

O175

贾高, 熊雅. 次椭圆Laplace算子特征值的迹公式[J]. J4, 2010, 48(06): 899-902.

GU Gao, XIONG Ya. Trace Formula of Eigenvalues of Subelliptic Laplacian[J]. J4, 2010, 48(06): 899-902.