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.