$n$-widths and Approximation theory on Compact Riemannian Manifolds

Abstract

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.

Published in Commutatitive and Noncommutative Harmonic Analysis, in Contemporary Mathematics. http://dx.doi.org/10.1090/conm/603/12043. arXiv admin note: substantial text overlap with arXiv:1104.0632