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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 1, Pages 122–134
(Mi timm209)
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This article is cited in 6 scientific papers (total in 6 papers)
About the sharp Jackson–Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere
M. V. Deikalova Ural State University
Abstract:
The best constant $C_{nm}$ in the Jackson–Nikol'skii inequality between uniform and integral norms of algebraic polynomials of given total degree $n\ge0$ on the unit sphere $\mathbb S^{m-1}$ of the Euclidean space $\mathbb R^m$ is studied. Two-sided estimates for the constant $C_{nm}$ are obtained, which, in particular, give the order $n^{m-1}$ of its behavior with respect to $n$ as $n\to+\infty$ for a fixed $m$.
Keywords:
multidimensional Euclidean sphere, algebraic polynomials, Jackson–Nikol'skii inequality.
Received: 10.01.2009
Citation:
M. V. Deikalova, “About the sharp Jackson–Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 1, 2009, 122–134; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S129–S142
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https://www.mathnet.ru/eng/timm209 https://www.mathnet.ru/eng/timm/v15/i1/p122
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Abstract page: | 370 | Full-text PDF : | 119 | References: | 53 | First page: | 5 |
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