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| 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. |
| 关键词: 逆问题 Sturm-Liouville算子 一维扰动 |
| DOI： |
| 分类号:O175.1 |
| 基金项目: |
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| INVERSE EIGENVALUE PROBLEMS FOR STURM-LIOUVILLE OPERATORS WITH SINGULAR RANK ONE PERTURBATIONS |
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WU Xue-wen
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| Abstract: |
| 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. |
| Key words: inverse problem Sturm-Liouville operator rank one perturbation |
