Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/69781
Type: Artigo de periódico
Title: Orthogonal polynomials on the unit circle and chain sequences
Author: Costa, MS
Felix, HM
Ranga, AS
Abstract: Szego has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1, 1] by the transformation 2x = z + z(-1). In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [- 1, 1] using the transformation 2x = z(1/2) + z(-1/2) . We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1, 1] that can be seen as extensions of symmetric orthogonal polynomials on [-1, 1] satisfying a three-term recurrence formula with real coefficients {c(n)} and {d(n)}, where {d(n)} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w (vertical bar w vertical bar = 1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {c(n)} and {d(n)}. (C) 2013 Elsevier Inc. All rights reserved.
Subject: Orthogonal polynomials on the unit circle
Chain sequences
Pure points of a measure
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.jat.2013.04.009
Date Issue: 2013
Appears in Collections:Artigos e Materiais de Revistas Científicas - Unicamp

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