Optimal quadrature formulas for classes of functions with bounded mixed difference
type: Item
instance of: scholarly article
title: Optimal quadrature formulas for classes of functions with bounded mixed difference
zbMATH Open document ID: 0760.41017
DOI: 10.1007/BF01137073
author: V. V. Dubinin
published in: Mathematical Notes
publication date: 1992-06-25T00:00:00Z
review text: Let \(H^ r_{p,\ell}\) be the class of \(d\)-places periodic functions with the domain of periodicity \(\Omega=[0,1]^ d\), satisfying the conditions \(\| f(x)\|_{L_ p(\Omega)}\leq 1\), \(\|\Delta^ \ell_ hf(x)\|_{L_ p}\leq\prod^ d_{j=1}| h_ j|^{r_ j}\), \(r=(r_ 1,\dots,r_ d)\), \(h=(h_ 1,\dots,h_ d)\), being the mixed difference of \(\ell\)th order. In the present paper the author gives optimal quadratures for such functions.
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 7977
zbMATH Keywords: optimal quadratures
reviewed by: Borislav Crstici
MaRDI profile type: Publication
cites work: Q5723455
cites work: Applications of Number Theory to Numerical Analysis
cites work: Reconstruction of periodic functions of several variables with respect to the values in the nodes of number-theoretic nets
full work available at URL: https://doi.org/10.1007/bf01137073
OpenAlex ID: W1990773656
description: scientific article; zbMATH DE number 7977