A unified approach to various orthogonalities
type: Item
instance of: scholarly article
title: A unified approach to various orthogonalities
zbMATH Open document ID: 0773.42016
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1993-08-31T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73304
review text: Within the framework of biorthogonal polynomials in the sense of the book ``Biorthogonality and its applications to numerical analysis'' (1992; Zbl 0757.41001) by the same author, the special case of vector orthogonal polynomials of dimension \(d=-1\) is investigated. Recurrence relations, a Christoffel-Darboux-type formula, and a Favard theorem is presented for this type of orthogonal polynomials. The analysis belongs to the formal theory. It is shown that the basic definition covers denominator polynomials of Laurent-Padé and two-point Padé approximants. For these polynomials the study therefore gives a unified approach.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 404398
zbMATH Keywords: biorthogonality
zbMATH Keywords: recurrence relations
zbMATH Keywords: vector orthogonal polynomials
zbMATH Keywords: Christoffel-Darboux-type formula
zbMATH Keywords: Favard theorem
zbMATH Keywords: Laurent-Padé and two- point Padé approximants
author: Claude Brezinski
reviewed by: Herbert Stahl
describes a project that uses: na3
MaRDI profile type: Publication
OpenAlex ID: W2067169163
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cites work: Orthogonal polynomials
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DOI: 10.5802/AFST.749
description: scientific article; zbMATH DE number 404398