Approximation of functions by Fourier-Laguerre sums
type: Item
instance of: scholarly article
title: Approximation of functions by Fourier-Laguerre sums
zbMATH Open document ID: 0844.42013
DOI: 10.1007/BF02309143
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: Let \(L_n^\alpha(x)\) \((n= 0, 1,\dots)\) be an orthogonal system of Laguerre polynomials and \[ f(x)= \sum_{k= 0}^\infty b_k(f) L_n^\alpha(x) \] the Fourier-Laguerre series for \(f\in L_2= L_2(R; \exp(- x) x^\alpha)\) \((\{\alpha\}>- \frac 12)\). Using estimates of the partial sums of Fourier-Laguerre series and the generalized shift operator \(f_h\), two sided estimates of the Kolmogorov \(n\)-diameter of \(D_n(W_\omega^r(D), L_2)\), where \(\omega(t)\) is an arbitrary modulus of continuity and \(D\) is the Laguerre differential operator, are given.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 846473
zbMATH Keywords: Fourier-Laguerre sums
zbMATH Keywords: Fourier-Laguerre series
zbMATH Keywords: generalized shift operator
zbMATH Keywords: Kolmogorov \(n\)-diameter
author: V. A. Abilov
reviewed by: B. P. Osilenker
MaRDI profile type: Publication
cites work: Another Note on Laguerre Polynomials
description: scientific article; zbMATH DE number 846473