On a finite moment perturbation of linear functionals and the inverse Szego transformation

Abstract

Given a sequence of moments {cn}n∈ℤ associated with an Hermitian linear functional L defined in the space of Laurent polynomials, we study a new functional L which is a perturbation of L in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of L, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming L is positive definite, the perturbation is analyzed through the inverse Szego transformation.

Edinson Fuentes

Instructor