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 Maddede Bu Makale
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Amaç & Hipotez:In this paper, an approach for studying inverse Sturm--Liouville problems with integrable potentials on finite intervals is presented.
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Temel Bulgular & Veri:In this paper, an approach for studying inverse Sturm--Liouville problems with integrable potentials on finite intervals is presented.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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