Inverse spectral problem for Jacobi matrices with partial spectral data

Abstract

The uniqueness and existence problems for a Jacobi matrix H are considered. Some uniqueness results are provided which imply that the Jacobi matrix H can completely be determined even if only partial entries are given on H together with partial information on the spectral data consisting of a subset of eigenvalues and norming constants (last components of normalized eigenvectors). Moreover, an existence result is established in terms of a set of eigenvalues and partial information on entries and norming constants.