边界条件依赖谱参数的非连续Sturm-Liouville算子的逆谱问题  

The inverse spectral problem for the Sturm-Liouville operators withboundary conditions dependent on spectral parameters

作　　者：闫丽 YAN Li(College of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2020年第3期1-7,共7页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金项目(11571212)。

摘　　要：目的为了丰富Sturm-Liouville(S-L)微分算子的逆谱理论,研究闭区间[0,1]上边界条件依赖谱参数的非连续S-L算子的逆谱问题。方法利用Weyl函数,借助谱映射的方法进行重构。结果与结论证明了相应的唯一性定理并给出实现势函数和边界参数的重构算法。Purposes—To enrich the inverse-spectrum theory of Sturm-Liouville(S-L)differential operators,and to study the inverse spectral problems for the S-L operators with the discontinuous conditions at an interior point and boundary conditions dependent on the eigenparameter on closed interval[0,1].Methods—Weyl function is used,and the spectral mapping method is adopted for reconstruction.Result and Conclusion—The uniqueness theorem is proved and the reconstruction algorithm of potential function and boundary parameter is given.

关 键 词：Sturm-Liouville微分算子 非连续条件 参数边界条件 重构算法 

分 类 号：O175.1[理学—数学]