一类幂零群上的特征值问题及估计

Eigenvalue Problem and Estimates for a Class of Nilpotent Lie Group

中文关键词:  谱  特征值估计

英文关键词:eigenvalue problem  Laplacian  nilpotent Lie group.

中文摘要:

      本文对幂零Lie群H_n×R^k上的Laplace算子,利用酉表示理论证明了它在全空间上无特征值存在,通过推广Friedrichs方法证明了在有界域上存在一列离散特征值,最后通过建立不变向量场之间的关系给出了特征值之差的估计.

英文摘要:

      In this paper we discuss the spectral properties of the Laplacian on the nilpotentLie group H_n×R^k.We show that the nonexistence of eigenvalue on the whole space by usingthe unitary representation theory and the existence of Dirichlet’s eigenvalue on the boundeddomain of H_n×R^k with the extension of Friedrichs'method to classical Laplacian.We alsogive the estimates of the gap by establishing some useful relation of invariant vector fields.