General Sobolev orthogonal polynomials
type: Item
instance of: scholarly article
title: General Sobolev orthogonal polynomials
zbMATH Open document ID: 0860.33007
author: Miguel A. Piñar
author: Francisco Marcellán
author: Teresa E. Pérez
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-23T00:00:00Z
review text: The authors derive properties of polynomials orthogonal with respect to the inner product \[ (f,g)=\langle u,fg\rangle+ \sum^N_{m=1} \lambda_m\langle u,f^{(m)} g^{(m)}\rangle, \] where the constant \(\lambda_m\) are nonnegative and \(u\) is a semiclassical, positive definite linear functional, so called Sobolev orthogonal polynomials. The connection between these polynomials and the semiclassical orthogonal polynomials with respect to the functional \(u\) is investigagted. Furthermore, algebraic and differential properties are obtained. Some examples illustrating the general considerations are added.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 908594
zbMATH Keywords: Sobolev orthogonal polynomials
zbMATH Keywords: semiclassical orthogonal polynomials
reviewed by: Hans-Jürgen Glaeske
MaRDI profile type: Publication
OpenAlex ID: W2034721430
DOI: 10.1006/JMAA.1996.0227
description: scientific article; zbMATH DE number 908594