通过柯西问题求解含Dirac权的逆Sturm-Liouville问题
Solving Inverse Dirac-weighted Sturm-Liouville Problems via Cauchy problems
- Department of Mathematics, Shandong University（山东大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文基于点相互作用方法，通过构造柯西问题显式重构带单点、两点及多点Dirac权的正则Sturm-Liouville问题的势函数，并讨论多点情形。
AI中文摘要：
基于我们先前工作中发展的点相互作用方法，本文研究带Dirac权的正则Sturm-Liouville问题的逆特征值问题。更确切地说，我们从一类柯西问题的解显式重构具有单点和两点Dirac权的正则Sturm-Liouville问题的势函数，该类柯西问题完全由源自量子力学中移动点相互作用模型的一族摄动问题的前几个特征值决定。最后，还讨论了多点Dirac权的情形。
英文摘要：
Building on the point interaction method developed in our previous work, this paper studies inverse eigenvalue problems for regular Sturm-Liouville problems with Dirac weights. More precisely, we explicitly reconstruct the potential of regular Sturm-Liouville problems with the single-point and two-point Dirac weights from the solutions of a class of Cauchy problems which is completely determined by the first eigenvalues of a family of perturbed problems originating from moving point interaction models in quantum mechanics. Finally, the multi-point Dirac weighted case is also discussed.
