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.