标题： 平面双调和算子的嵌入本征值的扰动 显示英文标题

标题： Perturbations of embedded eigenvalues for the planar bilaplacian

摘要： 在无界域上的算子可能会获得嵌入在本质谱中的特征值。 确定这些嵌入特征值在底层算子的小扰动下的命运是一个具有挑战性的任务，这种特征值的持续性性质与本质谱的重数紧密相关。 在本文中，我们考虑带有势的平面双调和算子，并证明在适当势空间中，使得嵌入特征值持续存在的势的集合是一个无限维流形，且具有无限余维。 显示英文摘要

摘要： Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues is linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials.