Best approximation of functions like \(| x|^\lambda\exp (-A| x|^{-a})\)
type: Item
instance of: scholarly article
title: Best approximation of functions like \(| x|^\lambda\exp (-A| x|^{-a})\)
zbMATH Open document ID: 0909.41018
published in: Journal of Approximation Theory
publication date: 1998-10-28T00:00:00Z
review text: The author determines the exact orders of best approximation by polynomials and by entire functions of exponential type for the functions: \(\varphi_{\lambda, \alpha,0} (x)= x^\lambda \exp (-Ax^{-\alpha)}\), for \(x>0\), and \(=0\) for \(x\leq 0\); \(\varphi_{\lambda, \alpha,i} (x)= (\text{sgn} x)^{i+1} | x|^\lambda \exp(-A| x|^{-\alpha})\), \(i=1,2\); \(\varphi_{\lambda, \alpha,3} (x)=(a^2-x^2)^\lambda \cdot \exp (-A((a+x)^{-\alpha}+ (a-x)^{-\alpha}))\), for \(| x|<a\), and \(=0\) for \(| x| \geq a\).
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1197038
zbMATH Keywords: best approximation
zbMATH Keywords: entire functions of exponential type
author: Michael I. Ganzburg
reviewed by: Costică Mustăţa
MaRDI profile type: Publication
full work available at URL: jath.1997.3131
OpenAlex ID: W2215443656
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DOI: 10.1006/JATH.1997.3131
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description: scientific article; zbMATH DE number 1197038