Estimates of Kolmogorov, Gelfand and linear 𝑛-widths on compact Riemannian manifolds

Abstract

We determine lower and exact estimates of Kolmogorov, Gelfand and linear n n -widths of unit balls in Sobolev norms in L p L_{p} -spaces on compact Riemannian manifolds. As it was shown by us previously these lower estimates are exact asymptotically in the case of compact homogeneous manifolds. The proofs rely on two-sides estimates for the near-diagonal localization of kernels of functions of elliptic operators.