The multidimensional Jackson theorem in \(L_ p\)
type: Item
instance of: scholarly article
title: The multidimensional Jackson theorem in \(L_ p\)
zbMATH Open document ID: 0780.42012
DOI: 10.1007/BF01247654
published in: Mathematical Notes
publication date: 1993-04-01T00:00:00Z
review text: The approximation of \(2\pi\)-periodic functions in several variables is investigated by trigonometric polynomials from the so-called hyperbolic cross. This means roughly, that one can only use trigonometric polynomials which contain only terms with the property that the product of the frequencies (in each variable) is bounded by a number \(n\), and the question is the behavior of this best approximant when \(n\to\infty\) (recall, that in the classical case the \textit{sum} of the frequences is bounded by \(n)\). In the paper under review the author gives an estimate for the best \(L_ p\)-approximation by trigonometric polynomials from the hyperbolic cross. The exact definitions are too involved to be recorded here.
Mathematics Subject Classification ID: 42B05
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 148620
zbMATH Keywords: best approximation
zbMATH Keywords: approximation of \(2\pi\)-periodic functions in several variables
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: hyperbolic cross
author: N. N. Pustovoĭtov
reviewed by: Vilmos Totik
MaRDI profile type: Publication
cites work: Q5337337
cites work: Multidimensional Jackson theorems
cites work: Approximation of functions of several variables by trigonometric polynomials with harmonics from hyperbolic crosses
description: scientific article; zbMATH DE number 148620