边界条件含有谱参数的非自伴不连续Sturm-Liouville算子的逆谱问题

Inverse spectral problems of the non-selfadjoint discontinuous Sturm-Liouville operator with boundary conditions dependent on spectral parameters

本文研究边界条件含有谱参数的非自伴不连续Sturm-Liouville算子的逆谱问题.首先利用基本解及其渐近估计,研究广义规范常数和广义谱数据;其次给出Weyl函数的表达式,得到广义谱数据,此数据唯一决定Weyl函数;最后给出势函数、边界条件参数和转移条件系数的重构算法.

In this paper,we study the inverse spectral problems of the non-selfadjoint discontinuous Sturm-Liouville operator with boundary conditions dependent on spectral parameters.Firstly,using the basic solutions and the asymptotic estimations,we give the generalized normal constant and generalized spectral data.Secondly,we prove the expression of the Weyl function and its corresponding uniqueness theorem.Finally,we design the reconstruction algorithms of the potential function,boundary condition parameters,and transmission condition coefficients.