Weighted best local \(L^ p\) approximation
type: Item
instance of: scholarly article
title: Weighted best local \(L^ p\) approximation
zbMATH Open document ID: 0567.41011
DOI: 10.1016/0021-9045(84)90034-0
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: For a weight w with some conditions near the origin the limit of the error \(\epsilon^{-n-1}\{f(\epsilon t)-P_{w,\epsilon}f(\epsilon t)\}\), where \(P_{w,\epsilon}f\) is the weighted best \(L^ p_{w,\epsilon}\) approximation of the function f in a class \(t^ p_{m,w}\), analogous to those considered by Calderón and Zygmund, is characterized. The limit is taken in a norm depending on \(\epsilon\) and, with additional assumptions on the weight, in a fixed norm.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3905151
zbMATH Keywords: algebraic polynomials
zbMATH Keywords: weighted best approximation
author: Roberto A. Macías
author: F. Zó
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90034-0
OpenAlex ID: W2080928668
cites work: Q3280291
cites work: Best \(L_2\) local approximation
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cites work: Tschebyscheff-Approximationen in kleinen Intervallen. I; II: Stetigkeitssätze für gebrochen rationale Approximationen
cites work: Q3864736
cites work: Q5577758
cites work: Interpolation and best \(L_ p \)local approximation
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description: scientific article; zbMATH DE number 3905151