Estimates of \(n\)-widths of Sobolev's classes on compact globally symmetric spaces of rank one. (Q1403850)

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.