Operators for one-side approximation by algebraic polynomials
type: Item
instance of: scholarly article
title: Operators for one-side approximation by algebraic polynomials
zbMATH Open document ID: 0674.41013
DOI: 10.1016/0021-9045(88)90017-2
author: Burkhard Lenze
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: Combining ideas of Freud and Nevai with a special interpolation problem of Hermite type the author constructs operators \(\phi_ n\) and \(\Phi_ n\) for the one-sided approximation of functions \(f\in BV[0,1]\). These operators are nonlinear and polynomial. The main result of the paper is a complete characterization and saturation theorem for these operators in the \(L_ p\)-metric, \(1\leq p\leq \infty\). It turns out that the saturation order is \(n^{-1/2}\). The appropriate measure for the smoothness of functions is here Popov's first order \(\tau\)-modulus of f with respect to p. The paper closes with a sufficient condition for a prescribed weighted approximation order in terms of the integration properties of a modified maximal function of f.
Mathematics Subject Classification ID: 41A40
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 4103670
zbMATH Keywords: one-sided approximation
zbMATH Keywords: saturation
zbMATH Keywords: maximal function
reviewed by: Manfred Wolfgang Müller
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90017-2
OpenAlex ID: W2042436525
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description: scientific article; zbMATH DE number 4103670