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arXiv · 1307.4056

Inverse Bernstein inequalities and min-max-min problems on the unit circle

Tamás Erdélyi·Douglas P. Hardin·Edward B. Saff
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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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Tamás Erdélyi, Douglas P. Hardin, Edward B. Saff. 2013-07-15. Inverse Bernstein inequalities and min-max-min problems on the unit circle. https://doi.org/10.1112/s0025579314000138

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