Semiorthogonal functions and orthogonal polynomials on the unit circle
type: Item
instance of: scholarly article
title: Semiorthogonal functions and orthogonal polynomials on the unit circle
zbMATH Open document ID: 0944.42017
DOI: 10.1016/S0377-0427(98)00140-X
author: M. Alfaro
author: María-José Cantero
author: L. Moral
published in: Journal of Computational and Applied Mathematics
publication date: 2000-09-17T00:00:00Z
review text: Let \(\mathcal P=\mathbb R[x]\) be the linear space of polynomials with real coefficients, \(\Sigma=\mathcal P[\sqrt{1-x^2}]\), and \(L\) be the space of Laurent polynomials with complex coefficients. To each Hermitian functional \(\mathcal L\) on \(L\) corresponds a functional \(\mathcal M_{\mathcal L}\) on \(\Sigma\), establishing a bijection. The authors construct a basis of \(\Sigma\) satisfying orthogonality conditions with respect to \(\mathcal M_{\mathcal L}\), and show its connection with \(2 \times 2\) matrix polynomials and polynomials orthogonal on the unit circle. The result is applied to the study of the rational modifications of Hermite functionals \(\mathcal L\) of the type \[ \widetilde{\mathcal L}=\left(\tfrac 12 (x+x^{-1})-a\right)\mathcal L , \quad a \in \mathbb R . \]
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1326351
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: matrix polynomials
zbMATH Keywords: moment functionals
reviewed by: Andrei Martínez Finkelshtein
MaRDI profile type: Publication
full work available at URL: s0377-0427(98)00140-x
OpenAlex ID: W2085213452
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description: scientific article; zbMATH DE number 1326351