Kolmogorov and Linear Widths of Balls in Sobolev Spaces on Compact Manifolds
Kolmogorov and Linear Widths of Balls in Sobolev Spaces on Compact Manifolds
We determine upper asymptotic estimates of Kolmogorov and linear $n$-widths of unit balls in Sobolev 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: …