论文标题
逆方形奇异点和征素分依赖的边界条件是同一枚硬币的两个侧面
Inverse square singularities and eigenparameter dependent boundary conditions are two sides of the same coin
论文作者
论文摘要
我们表明，可以将逆平方奇异性视为包含特征值参数的有理Herglotz的边界条件，其中“负极数量”。更确切地说，我们以统一的方式处理具有逆平方奇异性的一维schrödinger操作员或每个端点的特征值参数的nevanlinna函数的边界条件，并定义了此类运营商之间的darboux-type变换。这些转换尤其使一个转换可以传递几乎所有来自特征参数依赖性边界条件的边界值问题的光谱转换给具有反平方奇异性的人，反之亦然。
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 Schrödinger 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.
