%0 Journal Article
%T $n$-widths and Approximation theory on Compact Riemannian Manifolds
%A Isaac Pesenson
%A Daryl Geller
%J Mathematics
%D 2014
%I arXiv
%X We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev and Besov norms in $L_{p}$-spaces on compact Riemannian manifolds. The proofs rely on estimates for the near-diagonal localization of the kernels of elliptic operators. We also summarize some of our previous results about approximations by eigenfunctions of elliptic operators on compact homogeneous manifolds.
%U http://arxiv.org/abs/1404.5035v2