On the Problem of Optimal Reconstruction

We find lower bounds for linear and Alexandrov's cowidths of Sobolev's classes on Compact Riemannian homogeneous manifolds $M^{d}$. Using these results we give an explicit solution of the problem of optimal reconstruction of functions from Sobolev's classes $W^{\gamma}_{p}(M^{d})$ in $L_{q}(M^{d})$, $1 \leq p \leq q \leq \infty$.