Szegő type polynomials and para-orthogonal polynomials
type: Item
instance of: scholarly article
title: Szegő type polynomials and para-orthogonal polynomials
zbMATH Open document ID: 1213.42092
author: R. L. Lamblém
author: A. Sri Ranga
author: J. H. McCabe
author: Miguel A. Piñar
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-07-20T00:00:00Z
review text: The authors consider Szegő-type polynomials with respect to a linear functional \(\mathcal{M}\) for which the moments \(\mathcal{M}[t^n]=\mu_{-n}\) are all complex, \(\mu_{-n}=\mu_{n}\) and the associated Toeplitz determinants \(D_n\neq 0\) for \(n\geq 0.\) Recurrence relations involving the Szegő-type polynomials and their inverted polynomials are proved. The authors introduce para-orthogonal polynomials and study their basic properties. In the second part of the paper, starting from the existence of polynomials similar to para-orthogonal polynomials, the authors derive sufficient conditions for the existence of Szegő-type polynomials. Finally, the authors give several interesting examples to justify their results.
reviewed by: Kh. Hessami Pilehrood
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 5757935
zbMATH Keywords: Szegő polynomials
zbMATH Keywords: para-orthogonal polynomials
zbMATH Keywords: three term recurrence
zbMATH Keywords: hypergeometric functions.
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.04.066
OpenAlex ID: W2061570444
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DOI: 10.1016/J.JMAA.2010.04.066
description: scientific article; zbMATH DE number 5757935