Sobolev-type orthogonal polynomials: The nondiagonal case
type: Item
instance of: scholarly article
title: Sobolev-type orthogonal polynomials: The nondiagonal case
zbMATH Open document ID: 0841.42013
published in: Journal of Approximation Theory
publication date: 1996-02-01T00:00:00Z
review text: The authors study polynomials orthogonal with respect to an inner product of the form \[ (P, Q)= \int_I P(x) Q(x) d\mu+ \mathbb{P}(c)^t A\mathbb{Q}(c), \] where \(\mu\) is a positive Borel measure on the interval \(I\subset \mathbb{R}\), \(A\) is a \((r+ 1)\times (r+ 1)\) positive semidefinite matrix, \(c\in \mathbb{R}\), \[ \mathbb{P}(x):= \begin{pmatrix} P(x)\\ P'(x)\\ \vdots\\ P^{(r)}(x)\end{pmatrix} \] and \(\mathbb{P}(x)^t\) its transpose. They give representation formulas in terms of kernel matrices and derive some general results concerning the zeros of the Sobolev-type orthogonal polynomials. These zeros are studied in much more detail in the \((2\times 2)\)-case. Moreover, in this \((2\times 2)\)-case the relative asymptotic behaviour of the Sobolev-type orthogonal polynomials is studied in detail.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 827937
zbMATH Keywords: relative asymptotics
zbMATH Keywords: zeros
zbMATH Keywords: Sobolev-type orthogonal polynomials
author: M. Alfaro
author: Francisco Marcellán
author: M. L. Rezola
author: A. Ronveaux
reviewed by: Roelof Koekoek
MaRDI profile type: Publication
full work available at URL: jath.1995.1121
OpenAlex ID: W1993194416
DOI: 10.1006/JATH.1995.1121
description: scientific article; zbMATH DE number 827937