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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 307974, 8 pages
http://dx.doi.org/10.1155/2013/307974
Research Article

-Coherent Pairs on the Unit Circle

1Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo 340, 28045 Colima, COL, Mexico
2Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain

Received 23 July 2013; Accepted 19 September 2013

Academic Editor: Jinde Cao

Copyright © 2013 Luis Garza et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A pair of Hermitian regular linear functionals on the unit circle is said to be a -coherent pair if their corresponding sequences of monic orthogonal polynomials and satisfy , , , where . In this contribution, we consider the cases when is the linear functional associated with the Lebesgue and Bernstein-Szegő measures, respectively, and we obtain a classification of the situations where is associated with either a positive nontrivial measure or its rational spectral transformation.