Title

An Extremal Problem And An Estimation Of The Wronskian Of Certain Jacobi Polynomials

Keywords

Extremal problem; Jacobi polynomials; Maximum; Wronskian

Abstract

We study an extremal problem related to "splitted" Jacobi weights: For α, β > 0, find the largest value of max x∈[-1, 1] [(1 + x)β pm(x)2 + (1 - x)αqn(x)2] among all polynomials pm and qn of degree at most m and n, respectively, satisfying ∫1-1 [(1 + x) β pm(x)2 + (1 - x α qn(x)2] dx = 1. We show that the solution of this problem is related to an estimation of the Christoffel functions and the Wronskians associated with certain Jacobi polynomials. © 2002 Elsevier Science B.V. All rights reserved.

Publication Date

4-1-2003

Publication Title

Journal of Computational and Applied Mathematics

Volume

153

Issue

1-2

Number of Pages

311-320

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0377-0427(02)00633-7

Socpus ID

0037385983 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0037385983

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