ABSTRACT
We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that a Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. As a corollary, we obtain semi-infinite Jacobi analog of Marchenko's inverse spectral theorem for Schödinger operators, i.e. a Jacobi operator can be uniquely recovered from the Weyl m-function (or the spectral measure). We also solve our Borg–Marchenko-type problem under some conditions on two spectra, when missing part of the second spectrum and known norming constants have different index sets.
Disclosure statement
No potential conflict of interest was reported by the author(s).