The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case

Abstract

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.

26 pages. Changes in the presentation of some results

References in corpus (3)

• On Local Borg-Marchenko Uniqueness Results
• Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation
• The inverse problem for perturbed harmonic oscillator on the half-line with Dirichlet boundary conditions

Cited by in corpus (4)

• Inverse problems for Jacobi operators I: Interior mass-spring perturbations in finite systems
• Inverse problems for Jacobi operators IV: Interior mass-spring perturbations of semi-infinite systems
• The Hahn-Exton $q$-Bessel function as the characteristic function of a Jacobi matrix
• Ambarzumian-type problems for discrete Schrödinger operators