Estimates of n-widths of Sobolev's classes on compact globally symmetric spaces of rank one

Abstract

Estimates of Kolmogorov's and linear n-widths of Sobolev's classes on compact globally symmetric spaces of rank 1 (i.e. on S d , P d( R) , P d( C) , P d( H) , P 16(Cay)) are established. It is shown that these estimates have sharp orders in different important cases. New estimates for the ( p, q)-norms of multiplier operators Λ={λ k} k∈ N are given. We apply our results to get sharp orders of best polynomial approximation and n-widths.