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Turkish Journal of Mathematics

DOI

10.3906/mat-1911-79

Abstract

We develop a general method to calculate entropy and $n$-widths of sets of smooth functions on an arbitrary compact homogeneous Riemannian manifold $% \mathbb{M}^{d}$. Our method is essentially based on a detailed study of geometric characteristics of norms induced by subspaces of harmonics on $% \mathbb{M}^{d}$. This approach has been developed in the cycle of works [1, 2, 10-19]. The method's possibilities are not confined to the statements proved but can be applied in studying more general problems. As an application, we establish sharp orders of entropy and $n$-widths of Sobolev's classes $W_{p}^{\gamma }\left( \mathbb{M}^{d}\right) $ and their generalisations in $L_{q}\left( \mathbb{M}% ^{d}\right) $ for any $1

First Page

167

Last Page

184

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Mathematics Commons

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