Sturm-Liouville算子的一维奇异扰动的逆特征值问题  

INVERSE EIGENVALUE PROBLEMS FOR STURM-LIOUVILLE OPERATORS WITH SINGULAR RANK ONE PERTURBATIONS

作　　者：吴雪雯 WU Xue-wen(School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710072,China)

机构地区：[1]西北工业大学数学与统计学院,陕西西安710072

出　　处：《数学杂志》2021年第5期435-439,共5页Journal of Mathematics

摘　　要：本文研究了Sturm-Liouville算子的一维奇异扰动的逆特征值的问题.利用SturmLiouville算子的逆谱理论中的方法,获得了由Sturm-Liouville算子及其一维扰动的谱可以重构势函数的结果,推广了实数列成为扰动后算子的谱的充要条件的结论.This paper is concerned with the inverse eigenvalue problem for Sturm-Liouville operators with singular rank one perturbations.The result that the potential function can be reconstructed from the spectra of a Sturm-Liouville operator and the perturbation is obtained,by applying the method in the inverse spectral theory of Sturm-Liouville differential operators.The conclusion about a necessary and sufficient condition for a sequence of real numbers to be the spectrum of the perturbation is generalized.

关 键 词：逆问题 STURM-LIOUVILLE算子 一维扰动 

分 类 号：O175.1[理学—数学]