2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168940We 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 resultsMathematical Physics47B36, 49N45, 81Q10, 47A75, 47B37, 47B39text