A study of the generalized Christoffel functions with applications
type: Item
instance of: scholarly article
title: A study of the generalized Christoffel functions with applications
zbMATH Open document ID: 0965.42015
published in: Methods and Applications of Analysis
publication date: 2001-07-25T00:00:00Z
review text: The authors investigate the following minimization problem: Let \(f_1,f_2,\ldots,f_m\) be \(m\) linear functionals defined for polynomials and \(m \leq n\). Find the minimum of the quadratic form \(\|P\|^2 = \int_0^{2\pi} |P(e^{i\theta})|^2 d\mu(\theta)\) among all polynomials \(P\) of degree at most \(n\) for which \(f_1(P)=a_1, f_2(P)=a_2,\dots,f_m(P)=a_m\), where \(a_1,\ldots,a_m\) are given complex numbers. First they handle the case when \(m=1\) and then they give the solution for general \(m \leq n\) in terms of determinants containing the solutions with \(m=1\).
reviewed by: Walter Van Assche
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1513199
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Christoffel functions
author: E. Berriochoa
author: A. Cachafeiro
author: Francisco Marcellán
MaRDI profile type: Publication
full work available at URL: maa.1999.v6.n3.a4
OpenAlex ID: W2116935948
DOI: 10.4310/MAA.1999.V6.N3.A4
description: scientific article; zbMATH DE number 1513199