2 research outputs found
On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices
We present results on the unique reconstruction of a semi-infinite Jacobi
operator from the spectra of the operator with two different boundary
conditions. This is the discrete analogue of the Borg-Marchenko theorem for
Schr{\"o}dinger operators in the half-line. Furthermore, we give necessary and
sufficient conditions for two real sequences to be the spectra of a Jacobi
operator with different boundary conditions.Comment: In this slightly revised version we have reworded some of the
theorems, and we updated two reference
The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case
We present a technique for reconstructing a semi-infinite Jacobi operator in
the limit circle case from the spectra of two different self-adjoint
extensions. Moreover, we give necessary and sufficient conditions for two real
sequences to be the spectra of two different self-adjoint extensions of a
Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result