On Chebyshev-Markov rational functions over several intervals
type: Item
instance of: scholarly article
title: On Chebyshev-Markov rational functions over several intervals
zbMATH Open document ID: 0926.41012
published in: Journal of Approximation Theory
publication date: 1999-11-21T00:00:00Z
review text: The following extremal problem \[ \min_{c_1,c_2,\dots,c_n\in R} \bigg\| \frac {x^n+ c_1x^{n-1}+\dots +c_n} {\omega_n(x)} \bigg\| _{C(K)} \] where \(K\) is a compact subset of \(\mathbb R\) and \(\omega_n(x)\) is a fixed real polynomial of degree less than \(n\) and positive on \(K\) is studied in this paper. The rational solutions of the given problem are Chebyshev-Markov rational functions. There is found a parametric representation of Chebyshev-Markov rational functions for \(K=[b_1,b_2]\cup [b_3,b_4]\cup \dots \cup [b_{2p-1},b_{2p}]\), \(-\infty < b_1\leq b_2<\dots < b_{2p-1}\leq b_{2p}<\infty \) in terms of Schottky-Burnside automorphic functions.
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 1241239
zbMATH Keywords: Chebyshev-Markov rational functions
zbMATH Keywords: extremal problem
zbMATH Keywords: Shottky-Burnside automorphic functions
author: Alexei Lukashov
reviewed by: Josef Kofroň
MaRDI profile type: Publication
full work available at URL: jath.1997.3225
OpenAlex ID: W2078414949
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DOI: 10.1006/JATH.1997.3225
description: scientific article; zbMATH DE number 1241239