A problem of Totik on fast decreasing polynomials
type: Item
instance of: scholarly article
title: A problem of Totik on fast decreasing polynomials
zbMATH Open document ID: 0894.41008
author: Arno B. J. Kuijlaars
author: Walter Van Assche
published in: Constructive Approximation
publication date: 1998-09-07T00:00:00Z
review text: The authors give a solution of the following problem on fast decreasing polynomials, posed some years ago by V. Totik: For given \(\beta>2\), determine the largest positive constant \(c\) such that there exists a sequence of polynomials \(p_n\in\Pi_n\) and a constant \(C\) satisfying \(p_n (0) =1\) and \(| p_n(x) |\leq C \exp (-cn | x|^\beta)\) for \(x\in [-1,1]\). The solution, i.e., the exact bound for the constant \(c\), is given implicitly using the solution of a certain integral equation, too complicated to be presented here.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 1129641
zbMATH Keywords: fast decreasing polynomials
zbMATH Keywords: integral equation
zbMATH Keywords: exact bound
reviewed by: Guido Walz
MaRDI profile type: Publication
full work available at URL: s003659900065
OpenAlex ID: W2060186259
DOI: 10.1007/S003659900065
description: scientific article; zbMATH DE number 1129641