Inverse nodal problems for Sturm–Liouville operators on quantum star graphs

Abstract

In this work, we study the nodal inverse problem for Sturm–Liouville operators on quantum star graphs. We show that the zeros of eigenfunctions characterize the potential, and we present a simple algorithm that enables us to approximate it. The method does not rely on a priori information about the asymptotic behavior of eigenvalues. We manage to reduce the problem to a family of constant coefficient eigenvalue problems that can be solved explicitly and contain enough information to recover the potential. We also consider the multiplicity of eigenvalues and their vanishing properties, which only hold generically.