We find the relations between Weyl solutions and $m_{j}$-functions of Sturm--Liouville problems, and by finding the connection between these and the solutions of second-order partial differential equations for transformation kernels associated with Sturm--Liouville operators, we prove the uniqueness of the solution of inverse problems.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, an approach for studying inverse Sturm--Liouville problems with integrable potentials on finite intervals is presented.
📊
Key Findings & Data:In this paper, an approach for studying inverse Sturm--Liouville problems with integrable potentials on finite intervals is presented.
💡
Conclusion & Impact:We find the relations between Weyl solutions and $m_{j}$-functions of Sturm--Liouville problems, and by finding the connection between these and the solutions of second-order partial differential equations for transformation kernels associated with Sturm--Liouville operators, we prove the uniqueness of the solution of inverse problems.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Inverse Sturm--Liouville problem · Weyl solutions · $m_{j}$-functions
Abstract
In this paper, an approach for studying inverse Sturm--Liouville problems with integrable potentials on finite intervals is presented. We find the relations between Weyl solutions and $m_{j}$-functions of Sturm--Liouville problems, and by finding the connection between these and the solutions of second-order partial differential equations for transformation kernels associated with Sturm--Liouville operators, we prove the uniqueness of the solution of inverse problems.
MOSAZADEH, S. (2017). A new approach to uniqueness for inverse Sturm-Liouville problems on finite intervals. Turkish Journal of Mathematics, Cilt: 41 - Sayı: 5, 1224–1234. https://ajindex.com/articles/723164