Orthogonal Laurent polynomials. A new algebraic approach

In this paper, some important algebraic aspects in the theory of orthogonal Laurent polynomials, such as the three-term recurrence relation, the Christoffel–Darboux identity or the Liouville–Ostrogradski formula, are revisited from the Riemann–Hilbert window. These topics are considered for general ordered Laurent polynomial sequences, and not only for the usual “balanced” cases. In addition, a connection with Szegö polynomials (orthogonal polynomials in the unit circle) is explored.