Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros
type: Item
instance of: scholarly article
title: Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros
zbMATH Open document ID: 0755.41017
DOI: 10.1007/BF01279024
author: Peter Borwein
author: Tamás Erdélyi
published in: Constructive Approximation
publication date: 1992-09-27T00:00:00Z
review text: A function of the form (1) \(f(z)=\omega\prod^ m_{j=1}(z-z_ j)^{r_ j}\) \(\omega\neq 0\), \(r_ j\in\mathbb{R}\) \((j=1,2,\dots,m)\) is said to be a generalized complex algebraic polynomial of (generalized) degree \(N=\sum^ m_{j=1}r_ j\). If \(r_ j>0\) are integers then \(f\) is an ordinary polynomial of degree \(N\). In the paper Remez-, Nikol'skij- and Markov-type inequalities are proved for polynomials (1) of degree at most \(N\) under the assumption \(\sum_{\{j:| z_ j|\leq 1\}}r_ j\leq K\), \(0\leq K\leq N\).
reviewed by: Tibor Šalát
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 61194
zbMATH Keywords: complex algebraic polynomial
zbMATH Keywords: Markov-type inequalities
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 61194