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INVERSE BERNSTEIN INEQUALITIES AND MIN–MAX–MIN PROBLEMS ON THE UNIT CIRCLE
Published online by Cambridge University Press: 13 August 2014
Abstract
We give a short and elementary proof of an inverse Bernstein-type inequality found by S. Khrushchev for the derivative of a polynomial having all its zeros on the unit circle. The inequality is used to show that equally-spaced points solve a min–max–min problem for the logarithmic potential of such polynomials. Using techniques recently developed for polarization (Chebyshev-type) problems, we show that this optimality also holds for a large class of potentials, including the Riesz potentials $1/r^{s}$ with
$s>0.$
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- Research Article
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- Copyright © University College London 2014
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