Inverse spectral problems for Bessel operators with interior transmission conditions

Abstract

We consider inverse spectral problems for Bessel operators on the unit interval subject to a class of discontinuity conditions. We prove uniqueness theorems for these inverse spectral problems. That is, we show that either the eigenvalues and the corresponding norming constants or two sets of eigenvalues for different boundary conditions uniquely determine the potential, the angular-momentum quantum number, the boundary conditions, and the discontinuity conditions.