$n$-widths and Approximation theory on Compact Riemannian Manifolds
Functional Analysis
2014-07-15 v2
Abstract
We determine upper asymptotic estimates of Kolmogorov and linear -widths of unit balls in Sobolev and Besov norms in -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.
Cite
@article{arxiv.1404.5035,
title = {$n$-widths and Approximation theory on Compact Riemannian Manifolds},
author = {Isaac Pesenson and Daryl Geller},
journal= {arXiv preprint arXiv:1404.5035},
year = {2014}
}
Comments
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