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Ural Mathematical Journal, 2020, Volume 6, Issue 2, Pages 87–94
DOI: https://doi.org/10.15826/umj.2020.2.009 (Mi umj129) 		 
Inequalities for algebraic polynomials on an ellipse

Tatiana M. Nikiforovaab

a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.15826/umj.2020.2.009
Abstract: The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci $\pm 1$ of the derivative of an algebraic polynomial with real coefficients normalized on the segment $[- 1,1]$.
Keywords: polynomial, Chebyshev polynomials, ellipse, segment, derivative of a polynomial, uniform norm.
Funding agency Grant number
Ural Mathematical Center
The work was performed as a part of research conducted in the Ural Mathematical Center.
Bibliographic databases:
Document Type: Article
Language: English
Citation: Tatiana M. Nikiforova, “Inequalities for algebraic polynomials on an ellipse”, Ural Math. J., 6:2 (2020), 87–94
Citation in format AMSBIB
\Bibitem{Nik20}
\by Tatiana~M.~Nikiforova
\paper Inequalities for algebraic polynomials on an ellipse
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 2
\pages 87--94
\mathnet{http://mi.mathnet.ru/umj129}
\crossref{https://doi.org/10.15826/umj.2020.2.009}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4194017}
\elib{https://elibrary.ru/item.asp?id=44611153}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85099554245}
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