Abstract
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 \(L_{q}(M^{d}), 1 \leq q \leq p \leq \infty\).
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Kushpel, A., Tozoni, S. On the Problem of Optimal Reconstruction. J Fourier Anal Appl 13, 459–475 (2007). https://doi.org/10.1007/s00041-006-6902-3
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DOI: https://doi.org/10.1007/s00041-006-6902-3