A Christoffel–Darboux formula and a Favard's theorem for orthogonal Laurent polynomials on the unit circle

摘要

Let {ϕk(z)}k=0∞ be the family of orthonormal Laurent polynomials on the unit circle which spans Δ in the “ordering” induced by p(n)=E[(n+1)/2]. From the three-term recurrence relation satisfied by {ϕk(z)}k=0∞ we deduce a Christoffel–Darboux formula. Particular examples are considered and a Favard-type theorem is proved. A connection with the ordering induced by p(n)=E[n/2] is also established.