Geodesic
An estimate of the geometric mean of the derivative of a polynomial in terms of its uniform norm on a closed interval
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 153-161 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 153-161. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a13/

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