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Matematicheskie Zametki, 2013, Volume 93, Issue 4, Pages 604–613
DOI: https://doi.org/10.4213/mzm10171 (Mi mzm10171) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A Sharp Markov Brothers-Type Inequality in the Spaces L∞ and L1 on the Segment

I. E. Simonov

Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg
Full-text PDF (529 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm10171
Abstract: The inequality between the uniform norm of the derivative of order ℓ of an algebraic polynomial of degree n and the L1-norm of the polynomial itself on a segment are studied. For all ℓ⩾(n−1)/3, the exact constant and the extremal polynomial are written out.
Keywords: Markov brothers' inequality, algebraic polynomial, trigonometric polynomial, Chebyshev polynomial, Legendre polynomial.
Received: 18.04.2012
English version:
Mathematical Notes, 2013, Volume 93, Issue 4, Pages 607–615
DOI: https://doi.org/10.1134/S0001434613030292
Bibliographic databases:
Document Type: Article
UDC: 517.518.862
Language: Russian
Citation: I. E. Simonov, “A Sharp Markov Brothers-Type Inequality in the Spaces L∞ and L1 on the Segment”, Mat. Zametki, 93:4 (2013), 604–613; Math. Notes, 93:4 (2013), 607–615
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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