Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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