Horváth-Type Theorems on a Star Graph with Mixed Boundary Conditions

Abstract

In this paper, we deal with some partial inverse problems for the Sturm–Liouville operator on a star graph with Robin and/or Dirichlet boundary conditions in pendant vertices. It is shown that if all but one of the potentials are known a priori, then Horvath-type theorems hold. Our method is based on the related theory about Weyl function and the growth of entire functions.