On a result by Geronimus
type: Item
instance of: scholarly article
title: On a result by Geronimus
zbMATH Open document ID: 1235.42001
DOI: 10.1134/S008154381105004X
author: A. G. Babenko
author: Yu. V. Kryakin
author: V. A. Yudin
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2011-11-02T00:00:00Z
review text: Let \(E_n(f)_L\) be best approximation in \(L(\pi)\) of \(2\pi\)-periodic function \(f\) from this space. The authors propose new proof the next \textit{J. Geronimus} theorem [Ann. Math. (2) 37, 483--517 (1936; Zbl 0015.01401)]. Let \(f_{n,q}(t):= \sin(n+1)t- 2q\sin t\), \(t\in\pi\), where \(n\in\mathbb{N}\), \(t\in\mathbb{R}\). Then for \(|q|\geq 1\), \(E_{n-1}(f_{n,q})_L= 8|q|\) and for \(|q|< 1\) equals \(4(1+ q)^2\).
reviewed by: Yuri A. Brudnyi
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 5966627
zbMATH Keywords: integral approximation
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: rational functions of least deviation
MaRDI profile type: Publication
cites work: Q4273944
cites work: On some extremal properties of polynomials
cites work: On the representation of extremal functions in the \(L^1\)-norm
description: scientific article; zbMATH DE number 5966627