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 Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 4, Pages 153–161 (Mi timm875)

An estimate of the geometric mean of the derivative of a polynomial in terms of its uniform norm on a closed interval

M. R. Gabdullin

Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg

Abstract: We study an estimate of the geometric mean of the derivative of an algebraic polynomial of degree at most $n$ in terms of its uniform norm on a closed interval. In the general case, we obtain close two-sided estimates for the best constant; the estimates describe the order growth of the constant with respect to $n$. In the case $n=2$, the best constant is found exactly.

Keywords: Markov's inequality, algebraic polynomials, Chebyshev polynomials.

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UDC: 517.518.86

Citation: M. R. Gabdullin, “An estimate of the geometric mean of the derivative of a polynomial in terms of its uniform norm on a closed interval”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 4, 2012, 153–161

Citation in format AMSBIB
\Bibitem{Gab12} \by M.~R.~Gabdullin \paper An estimate of the geometric mean of the derivative of a~polynomial in terms of its uniform norm on a~closed interval \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2012 \vol 18 \issue 4 \pages 153--161 \mathnet{http://mi.mathnet.ru/timm875} \elib{https://elibrary.ru/item.asp?id=18126478}