Inverse spectral problems for Sturm–Liouville operators with partial information

In this paper, we study the inverse spectral problems for Sturm–Liouville operators with Robin boundary conditions and show that if the potential q on the interval [ 0 , α ] for some α ∈ [ 0 , 1 ) is given a priori, then the potential q on the whole interval [ 0 , 1 ] can be uniquely determined by a subset of pairs of eigenvalues and the weight numbers of the corresponding eigenvalues or by parts of two spectra.