On time dependent orthogonal polynomials on the unit circle - Ben-Artzi, A.; Gohberg, I. C. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
Two index formulas for operators defined by infinite band matrices are proved. These results may be interpreted as a generalization of the classical theorem of M. G. Krein for orthogonal polynomials. The proofs are based on dichotomy and nonstationary inertia theory.