On orthogonal polynomials for certain nondefinite linear functionals
type: Item
instance of: scholarly article
title: On orthogonal polynomials for certain nondefinite linear functionals
zbMATH Open document ID: 0942.42014
DOI: 10.1016/S0377-0427(98)00150-2
author: Sven Ehrich
published in: Journal of Computational and Applied Mathematics
publication date: 2000-02-10T00:00:00Z
review text: Nondefinite linear functionals \(L_n[f]= \int_{\mathbb{R}} w(x) f^{(n)}(x) dx\), i.e., polynomials \(P_m\) of degree \(\leq m\) satisfying the relation \(\int_{\mathbb{R}} w(x)(P_m(x) x^k)^{(n)} dx= 0\) are considered. The problem is studied whether there exist polynomials \(P_m\) which satisfy the foregoing relation and all of whose zeros are real. Nonexistence of orthogonal polynomials with all zeros real in several cases are proved. The cases studied include different relations between \(w\), \(n\), and \(r\). The connection with moment preserving spline approximation is used for the proofs.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 1326361
zbMATH Keywords: nondefinite linear functionals
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: zeros
zbMATH Keywords: spline approximation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326361