Estimates of Kolmogorov, Gelfand and linear $n$-widths on compact Riemannian manifolds
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- by Isaac Z. Pesenson
- Proc. Amer. Math. Soc. 144 (2016), 2985-2998
- DOI: https://doi.org/10.1090/proc/13054
- Published electronically: March 1, 2016
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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.References
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Bibliographic Information
- Isaac Z. Pesenson
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- MR Author ID: 196903
- Email: pesenson@temple.edu
- Received by editor(s): August 30, 2015
- Published electronically: March 1, 2016
- Communicated by: Alexander Iosevich
- © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3487230