Eigenvalue asymptotics for polynomially compact pseudodifferenial operators and applications

具有长程势的Kramers-Fokker-Planck算子的谱性质

Spectral properties of the Kramers-Fokker-Planck operator with a long-range potential

本文研究带长程势的Kramers-Fokker-Planck算子的谱性质，证明阈值是特征值唯一可能的聚点、例外集外极限吸收原理成立，并刻画了离散与嵌入非阈值特征值对应特征函数的不同衰减速率。

双曲面在随机覆盖模型中的特征值刚性

Polynomial bounds for eigenfunctions and eigenvalues on random covers of hyperbolic surfaces

研究双曲面在随机覆盖模型中的特征值分布，证明其收敛于双曲平面的谱测度，改进了Monk的对数界，并提升了特征函数的L^∞界。

Spectral properties of the Neumann-Poincaré operator in 3D elasticity

We consider the double layer potential (Neumann-Poincaré) operator appearing in 3-dimensional elasticity. We show that the recent result about the polynomial compactness of this operator for the case of a homogeneous media follows without additional calculations from previous considerations by Agranovich et.al., based upon pseudodifferential operators. Further on, we define the NP operator for the case of a nonhomogeneous isotropic media and show that its properties depend crucially on the character of non-homogeneity. If the Lamé parameters are constant along the boundary, the NP operator is …

具有无限记忆的抽象强耦合双曲方程的衰减率与特征值渐近性

Decay Rates and Eigenvalue Asymptotics for Abstract Strongly Coupled Hyperbolic Equations with Infinite Memory

本文研究具有无限记忆的抽象强耦合双曲方程的渐近行为，通过频域分析证明单个记忆项可实现多项式镇定，并给出依赖于参数a的衰减率及特征值渐近式，验证其最优性。

三维光滑区域上弹性Neumann-Poincaré算子：多项式compactness和谱结构

Elastic Neumann-Poincaré operators on three dimensional smooth domains: Polynomial compactness and spectral structure

我们证明了定义在三维有界区域光滑边界上的弹性Neumann-Poincaré算子是多项式紧的，而该算子是非紧的。因此，我们证明了弹性Neumann-Poincaré算子的谱由三个非空的特征值序列组成，这些特征值序列累积到由Lamé参数确定的一定数目。利用曲面里斯变换、伪微分算子的微积分和谱映射定理证明了这些结果。