Estimates of Kolmogorov, Gelfand and linear n- widths on Compact Riemannian Manifolds

2015/08/30 by Pesenson, Isaac Z.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.04320

Abstract

We determine lower and exact estimates of Kolmogorov, Gelfand and linear n-widths of unit balls in Sobolev norms in 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.

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