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 defferential equations for transformation kernels associated with Sturm-Liouville operators‎, ‎we prove the uniqueness of the solution of inverse problems