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2013 ( 1,1 ) -Coherent Pairs on the Unit Circle
Luis Garza, Francisco Marcellán, Natalia C. Pinzón-Cortés
Abstr. Appl. Anal. 2013: 1-8 (2013). DOI: 10.1155/2013/307974

Abstract

A pair ( 𝒰 , 𝒱 ) of Hermitian regular linear functionals on the unit circle is said to be a ( 1,1 ) -coherent pair if their corresponding sequences of monic orthogonal polynomials { ϕ n ( x ) } n 0 and { ψ n ( x ) } n 0 satisfy ϕ n [ 1 ] ( z ) + a n ϕ n - 1 [ 1 ] ( z ) = ψ n ( z ) + b n ψ n - 1 ( z ) , a n 0 , n 1 , where ϕ n [ 1 ] ( z ) = ϕ n + 1 ( z ) / (n + 1) . In this contribution, we consider the cases when 𝒰 is the linear functional associated with the Lebesgue and Bernstein-Szegő measures, respectively, and we obtain a classification of the situations where 𝒱 is associated with either a positive nontrivial measure or its rational spectral transformation.

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Luis Garza. Francisco Marcellán. Natalia C. Pinzón-Cortés. " ( 1,1 ) -Coherent Pairs on the Unit Circle." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/307974

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1298.42030
MathSciNet: MR3126763
Digital Object Identifier: 10.1155/2013/307974

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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