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Estimates of Kolmogorov, Gelfand and linear $ n$-widths on compact Riemannian manifolds


Author: Isaac Z. Pesenson
Journal: Proc. Amer. Math. Soc. 144 (2016), 2985-2998
MSC (2010): Primary 43A85, 42C40, 41A17; Secondary 41A10
DOI: https://doi.org/10.1090/proc/13054
Published electronically: March 1, 2016
MathSciNet review: 3487230
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Abstract: We determine lower and exact estimates of Kolmogorov, Gelfand and linear $ n$-widths of unit balls in Sobolev norms in $ L_{p}$-spaces on compact Riemannian manifolds. As it was shown by us previously these lower estimates are exact asymptotically in the case of compact homogeneous manifolds. The proofs rely on two-sides estimates for the near-diagonal localization of kernels of functions of elliptic operators.


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Additional Information

Isaac Z. Pesenson
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: pesenson@temple.edu

DOI: https://doi.org/10.1090/proc/13054
Keywords: Compact manifold, Laplace-Beltrami operator, Sobolev space, eigenfunctions, kernels, $n$-widths
Received by editor(s): August 30, 2015
Published electronically: March 1, 2016
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2016 American Mathematical Society