A new approach to uniqueness for inverse Sturm-Liouville problems on finite intervals


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.

Keywords: Inverse Sturm--Liouville problem, Weyl solutions, $m_{j}$-functions, transformation kernel,

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