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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sharp estimates for Lebesgue constants
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by Marco Carenini and Paolo M. Soardi PDF
Proc. Amer. Math. Soc. 89 (1983), 449-452 Request permission

Abstract:

Suppose $C \subset {R^N}$ is a closed convex bounded body containing 0 in its interior. If $\partial C$ is sufficiently smooth with strictly positive Gauss curvature at each point, then, denoting by ${L_{r,C}}$ the Lebesgue constant relative to $C$, there exists a constant $A > 0$ such that ${L_{r,C}} \geqslant A{r^{(N - 1)/2}}$ for $r$ sufficiently large. This complements the known result that there exists a constant $B$ such that ${L_{r,C}} \leqslant B{r^{(N - 1)/2}}$ for $r$ sufficiently large.
References
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 449-452
  • MSC: Primary 42B05
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0715864-1
  • MathSciNet review: 715864