Abstract

We study the inverse spectral problem of reconstructing nonsplitting boundary conditions for the Sturm–Liouville operator from a minimal amount of spectral data. Necessary and sufficient conditions are derived for the existence of solutions of the problem under consideration and for these solutions to be isolated or nonisolated. We propose a simple analytical algorithm for reconstructing boundary conditions. (Explicit formulas are provided for the coefficients of the boundary conditions.) It is shown that the condition determining the properties of the problem is the dimension of the linear span of matrices of fundamental solution systems corresponding to the given spectral data.

中文翻译：

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从最小特征值集重构Sturm-Liouville算子的非分裂边界条件

摘要

我们研究了从最小的光谱数据中为Sturm-Liouville算子重建非分裂边界条件的逆光谱问题。得出了所考虑问题的解决方案的存在以及将这些解决方案隔离或非隔离的必要和充分条件。我们提出了一种简单的解析算法来重建边界条件。（为边界条件的系数提供了明确的公式。）表明，确定问题性质的条件是与给定光谱数据相对应的基本解系统的矩阵线性范围的维数。