Reconstruction formula for the potential function of Sturm-Liouville problem with eigenparameter boundary condition

Abstract

It is known that the uniqueness of potential function of the Sturm-Liouville problem can be shown from the nodal points. In this article, we solve the inverse nodal problem of the reconstruction of the potential function q from the nodal data by a pointwise limit. We show that this convergence is in the L-1. It is mentioned that this method is based on the works of Law and Yang, but we have applied the method for the Sturm-Liouville problem depending on eigenparameter boundary conditions.