On polynomials with positive coefficients
type: Item
instance of: scholarly article
title: On polynomials with positive coefficients
zbMATH Open document ID: 0653.41010
DOI: 10.1016/0021-9045(88)90119-0
author: Tamás Erdélyi
author: Jószef Szabados
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: The authors consider Lorentz polynomials with either non-negative or non- positive coefficients. Due to the non-uniqueness of representation in this class, the concept of the Lorentz degree is introduced and studied. Several theorems are proved concerning the Lorentz degree and the growth of Lorentz polynomials. For example, an estimate of the maximal Lorentz degree of all Lorentz polynomials with either non-negative or non- positive coefficients having no zeros in a certain open region in the complex plane containing (-1,1) is given. This is used to establish the (known) characterization that a polynomial not identically zero is a Lorentz polynomial with either non-negative or non-positive coefficients iff it has no roots in (-1,1).
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A29
zbMATH DE Number: 4065579
zbMATH Keywords: Lorentz polynomials
zbMATH Keywords: Lorentz degree
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90119-0
OpenAlex ID: W1989548804
cites work: The degree of approximation by polynomials with positive coefficients
cites work: Q5534403
cites work: Inequalities for derivatives of polynomials of special type
cites work: Inequalities for Derivatives of Polynomials With Restricted Zeros
description: scientific article; zbMATH DE number 4065579