标题： 波导远处扰动的谱的渐近行为 显示英文标题

标题： Asymptotic behaviour of the spectrum of a waveguide with distant perturbation

摘要： 我们考虑由n维管状结构建模的波导，其中考虑了Dirichlet拉普拉斯算子被两个远距离扰动所扰动。这些扰动由两个任意的抽象算子描述，它们在某种意义上是“局部化的”，并且它们的“支撑”之间的距离趋于无穷大。我们研究此类问题离散谱的渐近行为。主要结果是特征值的收敛定理和渐近展开式。还描述了相关特征函数的渐近行为。我们还提供了一些对应于远距离扰动特定选择的例子。这些例子包括势能、二阶微分算子、磁Schrodinger算子、弯曲和变形波导、delta相互作用和积分算子。 显示英文摘要

摘要： We consider the waveguide modelled by n-dimensional tube in which Dirichlet Laplacian is considered perturbed by two distant perturbations. These perturbations are described by two arbitrary abstract operators which are ''localized'' in some sense, and the distance between their ''supports'' tends to infinity. We study the asymptotic behaviour of the discrete spectrum of such problem. The main results are the convergence theorem and the asymptotics expansions for the eigenvalues. The asymptotic behaviour of the associated eigenfunctions is described as well. We also provide some examples corresponding to the particular choice of the distant perturbations. These examples are potential, second order differential operator, magnetic Schrodinger operator, curved and deformed waveguide, delta interaction, and integral operator.