Some extremal problems for algebraic polynomials in loaded spaces
type: Item
instance of: scholarly article
title: Some extremal problems for algebraic polynomials in loaded spaces
zbMATH Open document ID: 1191.33004
DOI: 10.3103/S1066369X10020064
published in: Russian Mathematics
publication date: 2010-02-19T00:00:00Z
review text: In [\textit{T. H. Koornwinder}, Can. Math. Bull. 27, 205--214 (1984; Zbl 0507.33005)] generalized Jacobi polynomials with respect to a Sobolev type inner product were introduced. Here the author computes their norm in a related space using this result that Zolotarev type extremal problems are solved in this space.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 5673450
zbMATH Keywords: Zolotarev extremal problem
zbMATH Keywords: Sobolev inner product
zbMATH Keywords: Jacobi polynomials
author: B. P. Osilenker
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
cites work: Discrete and continuous boundary problems
cites work: Q5769114
cites work: Q5807063
cites work: Estimates of polynomials orthogonal with respect to the Legendre-Sobolev inner product
cites work: A note on the Koekoeks' differential equation for generalized Jacobi polynomials
cites work: Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions
cites work: Differential Equations for Symmetric Generalized Ultraspherical Polynomials
cites work: Differential equations for generalized Jacobi polynomials
cites work: Orthogonal Polynomials With Weight Function (1 - x)α( l + x)β + Mδ(x + 1) + Nδ(x - 1)
cites work: Orthogonal polynomials satisfying fourth order differential equations
cites work: THE KRALL POLYNOMIALS: A NEW CLASS OF ORTHOGONAL POLYNOMIALS
cites work: Generalized trace formula and asymptotics of the averaged Turan determinant for polynomials orthogonal with a discrete Sobolev inner product
cites work: An extremal problem for algebraic polynomials in the symmetric discrete Gegenbauer--Sobolev space
full work available at URL: s1066369x10020064
OpenAlex ID: W2090249867
description: scientific article; zbMATH DE number 5673450