2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69357This work is in a stream initiated by a paper of Killip and Simon [Ann. of Math. (2003)]. Using methods of Functional Analysis and the classical Szegö Theorem we prove sum rule identities in a very general form. Then, we apply the result to obtain new asymptotics for orthonormal polynomials.Appendix was extendedSpectral TheoryMathematical Physics47B36text