Analysis of perturbations of moments associated with orthogonality linear functionals through the Szego transformation

Abstract

In this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [-1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the corresponding measure on the unit circle, when both measures are related through the Szegő transformation. A similar perturbation is analyzed through the inverse Szego transformation. In both cases, we show that the applied perturbation can be expressed in terms of the singular part of the measures, and also in terms of the corresponding sequences of moments.

Edinson Fuentes

Instructor