论文标题
椭圆形伪差异操作员对紧凑型谎言组的本征函数总和的估计值
Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups
论文作者
论文摘要
我们将Donnelly和Fefferman以及Lebeau和Robbiano证明的估计值扩展了Laplacian（紧凑型歧管上）的本征函数的总和，以估计任何正面和椭圆形伪二分差异级别的正常级别均分化的二分级算子的特征函数的总和。我们的标准是根据操作员的相应矩阵值符号的积极性强加的。作为对控制理论中这些不平等的应用，我们为椭圆形伪差异操作员的扩散模型的无量控制性获得了紧凑的谎言组。
We extend the estimates proved by Donnelly and Fefferman and by Lebeau and Robbiano for sums of eigenfunctions of the Laplacian (on a compact manifold) to estimates for sums of eigenfunctions of any positive and elliptic pseudo-differential operator of positive order on a compact Lie group. Our criteria are imposed in terms of the positivity of the corresponding matrix-valued symbol of the operator. As an application of these inequalities in the control theory, we obtain the null-controllability for diffusion models for elliptic pseudo-differential operators on compact Lie groups.
