标题： 奇异的平方反比项和依赖特征值的边界条件是同一枚硬币的两面 显示英文标题

标题： Inverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin

摘要： 我们证明反平方奇点可以被视为包含与特征值参数相关的有理Herglotz–Nevanlinna函数的边界条件，且“极点数为负数”。 更准确地说，我们以统一的方式处理一维Schrödinger算子，这些算子在每个端点处要么具有反平方奇点，要么具有包含与特征值参数相关的有理Herglotz–Nevanlinna函数的边界条件，并定义此类算子之间的Darboux型变换。 这些变换特别允许将几乎任何谱结果从具有特征值相关边界条件的边值问题转移到具有反平方奇点的问题，反之亦然。 显示英文摘要

摘要： We show that inverse square singularities can be treated as boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter with "a negative number of poles". More precisely, we treat in a unified manner one-dimensional Schr\"{o}dinger operators with either an inverse square singularity or a boundary condition containing a rational Herglotz--Nevanlinna function of the eigenvalue parameter at each endpoint, and define Darboux-type transformations between such operators. These transformations allow one, in particular, to transfer almost any spectral result from boundary value problems with eigenparameter dependent boundary conditions to those with inverse square singularities, and vice versa.