Heisenberg群上Folland-Stein算子的Dirichlet特征值问题

On the Dirichlet Eigenvalue Problem of the Folland-Stein Operator on the Heisenberg Group

该文研究Heisenberg群上Folland－Stein算子■（α为复数）的特征值问题，证明了当|Reα|＜n时，■具离散分布的特征值．当α∈（-n,n）时，特征值均为正的．然后给出了相邻特征值之差的估计．

We study the Dirichlet eigenvalue problem of the Folland-Stein operator which has discrete eigenvalues as |Reα|＜n and positive eigenvalues as α∈(- n,n). Then by establishing the Rayleigh Theorem and the Min-Max Theorem we give the estimates for the differences of the consecutive eigenvalues.