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Revista Integración
versión impresa ISSN 0120-419X
Resumen
FUENTES, EDINSON y 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 {cn}n∈ℤ associated with an Hermitian linear functional L defined in the space of Laurent polynomials, we study a new functional LΩ 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 LΩ, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming LΩ is positive definite, the perturbation is analyzed through the inverse SzegŐ transformation.
Palabras clave : Orthogonal polynomials on the unit circle; perturbation of moments; inverse SzegŐ transformation.