On a.e. convergence of Durrmeyer-Stieltjes polynomials
type: Item
instance of: scholarly article
title: On a.e. convergence of Durrmeyer-Stieltjes polynomials
zbMATH Open document ID: 0806.41017
published in: Journal of Approximation Theory
publication date: 1994-09-27T00:00:00Z
review text: Let \(\nu\) be a finite Borel measure on \([0,1]\). The Durrmeyer-Stieltjes operators are defined by \[ D_ n\nu= (n+1) \sum^ n_{k=0}\left( \int^ 1_ 0 N_{k,n}(t)d\nu\right)N_{k,n}\quad (n\in\mathbb{N}), \] where \(N_{k,n}\) stands for the \(k\)th Bernstein polynomial of degree \(n\). The main results of this paper can be summarized as follows: 1. The maximal operator of the sequence \(\{D_ n\}\) is of weak type. 2. The sequence \(\{D_ n\nu\}\) converges a.e. on \([0,1]\) to the absolutely continuous part of the measure \(\nu\).
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 645056
zbMATH Keywords: integral operators
zbMATH Keywords: maximal operator
author: László Szili
reviewed by: Edward Neuman
MaRDI profile type: Publication
full work available at URL: jath.1994.1112
OpenAlex ID: W1967721309
DOI: 10.1006/JATH.1994.1112
description: scientific article; zbMATH DE number 645056