On trigonometric n-widths and their generalization
type: Item
instance of: scholarly article
title: On trigonometric n-widths and their generalization
zbMATH Open document ID: 0543.41027
DOI: 10.1016/0021-9045(84)90092-3
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: The author proves that the subspaces of the form \(span\{e^{ik_ 1.},...,e^{ik_ n.}\}\), with certain \(k_ 1,...,k_ n\in {\mathbb{Z}}\), are asymptotically optimal for the n-widths of the Sobolev classes \(W^ r_ p\) in \(L_ q (1\leq p\leq 2\leq q<\infty\), \(r>p^{-1}-q^{-1})\). For \(r>1/p+1/2\) this fact was established by \textit{V. E. Maiorov} [Math. USSR, Sb. 41, 361-382 (1982; Zbl 0478.41017)]. The proof is based on a probability argument and is derived from a more general statement for functions representable as convolutions on a compact Abelian group.
Mathematics Subject Classification ID: 41A46
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 3863798
zbMATH Keywords: n-widths
zbMATH Keywords: Sobolev classes
zbMATH Keywords: convolutions
zbMATH Keywords: compact Abelian group
author: Yuly Makovoz
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90092-3
OpenAlex ID: W1983644830
cites work: DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
cites work: On some properties of orthogonal systems of convergence
cites work: Q3930220
cites work: ON LINEAR WIDTHS OF SOBOLEV CLASSES AND CHAINS OF EXTREMAL SUBSPACES
cites work: On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
cites work: Approximationszahlen von Sobolev-Einbettungen
description: scientific article; zbMATH DE number 3863798