1 Kolmogorov and Linear Widths of Balls in Sobolev and Besov Norms on Compact Manifolds

Details 1 Kolmogorov and Linear Widths of Balls in Sobolev and Besov Norms on Compact Manifolds 1 Kolmogorov and Linear Widths of Balls in Sobolev and Besov Norms on Compact Manifolds

2011-04-04

arxiv.org/abs/1104.0632v1

Mathematics

Functional Analysis

28 pages

Scientific paper

We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev and Besov norms in $L_{p}$-spaces on smooth compact Riemannian manifolds. For compact homogeneous manifolds, we establish estimates which are asymptotically exact, for the natural ranges of indices. The proofs heavily rely on our previous results such as: estimates for the near-diagonal localization of the kernels of elliptic operators, Plancherel-Polya inequalities on manifolds of bounded geometry, cubature formulas with positive coefficients and uniform estimates on Clebsch-Gordon coefficients on general compact homogeneous manifolds.

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