On the positivity of some bilinear functionals in Sobolev spaces
type: Item
instance of: scholarly article
title: On the positivity of some bilinear functionals in Sobolev spaces
zbMATH Open document ID: 0929.42014
DOI: 10.1016/S0377-0427(99)00063-1
author: André Draux
author: Charaf El Hami
published in: Journal of Computational and Applied Mathematics
publication date: 1999-11-10T00:00:00Z
review text: Let \(c^{(m)}\) define a positive definite inner product and \(a(f,g)=\sum_{m=0}^N\lambda_mc^{(m)}(f^{(m)},g^{(m)})\) a bilinear functional. The authors study the domain of \(\{\lambda_m\}\) leading to the positivity of \(a(p,p)\), where \(p\) are polynomials of degree \(n\). The cases of Hermite, Laguerre, Gegenbauer and Jacobi are analysed with help of symbolic computations with Mathematica. For \(N=1\), the Markov-Bernstein inequalities are given.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 1326531
zbMATH Keywords: formal orthogonal polynomials
zbMATH Keywords: zeros of polynomials
describes a project that uses: Mathematica
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00063-1
OpenAlex ID: W2096208426
description: scientific article; zbMATH DE number 1326531