Estimates of \(n\)-widths of Sobolev's classes on compact globally symmetric spaces of rank one.
type: Item
instance of: scholarly article
title: Estimates of \(n\)-widths of Sobolev's classes on compact globally symmetric spaces of rank one.
zbMATH Open document ID: 1035.46022
DOI: 10.1016/S0022-1236(02)00167-2
published in: Journal of Functional Analysis
publication date: 2003-09-04T00:00:00Z
review text: In this paper, estimates of Kolmogorov's and linear \(n\)-widths of Sobolev's classes on compact globally symmetric spaces of rank one (i.e., on \(S^d\), \(P^d({\mathbb R})\), \(P^d({\mathbb C})\), \(P^d({\mathbb H})\), \(P^{16}\)(\textbf{Cay})) are established. It is shown that these estimates have sharp orders in different important classes. New estimates for the \((p,q)\)-norms of multiplier operators \(\Lambda ={\{{\lambda}_k\}}_{k\in \mathbb{N}}\) are also given and the authors apply the obtained results to get sharp orders of best polynomial approximation and \(n\)-widths.
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1974800
zbMATH Keywords: \(n\)-width
zbMATH Keywords: two point homogeneous manifold
zbMATH Keywords: Sobolev space
author: Benjamin Bordin
author: Alexander Kushpel
author: Jeremy Levesley
author: Sérgio A. Tozoni
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
cites work: Sommes De Cesaro Et Multiplicateurs Des Developpements en Harmoniques Spheriques
cites work: Q4250274
cites work: Fractional derivatives and best approximations
cites work: Q5820721
cites work: Q5539480
cites work: Q5734920
cites work: The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
cites work: On \(n\)-dimensional diameters of compacts in a Hilbert space
cites work: On Riesz's interpolational formula and Bernshtein's inequality for functions on homogeneous spaces
cites work: Q3660269
cites work: The Addition Formula for Jacobi Polynomials and Spherical Harmonics
cites work: Q5719437
cites work: Q3344608
cites work: Two-point homogeneous spaces
full work available at URL: s0022-1236(02)00167-2
OpenAlex ID: W1988955873
description: scientific article; zbMATH DE number 1974800