Abstract

FUENTES, EDINSON  and  GARZA, LUIS E. On a finite moment perturbation of linear functionals and the inverse SzegŐ transformation. Integración - UIS [online]. 2016, vol.34, n.1, pp.39-58. ISSN 0120-419X.  https://doi.org/10.18273/revint.v34n1-2016003.

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

Keywords : Orthogonal polynomials on the unit circle; perturbation of moments; inverse SzegŐ transformation.

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