Inverse Problem For Dirichlet Boundary Value Problems

Abstract: In this article we consider Sturm-Liouville operator with $q\in W_{1}^{2}[0,1]$ and Dirichlet boundary conditions. We prove that if the set ${(n\pi)^{2}:n\in \mathbb{N}}$ is a subset of the spectrum of the Sturm-Liouville operator with Dirichlet boundary conditions, then $q=0$ a.e.