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arXiv · 1509.04320

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

Isaac Z. Pesenson
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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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Isaac Z. Pesenson. 2015-08-30. Estimates of Kolmogorov, Gelfand and linear $n$- widths on Compact Riemannian Manifolds. https://arxiv.org/abs/1509.04320

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