INVERSE BERNSTEIN INEQUALITIES AND MIN–MAX–MIN PROBLEMS ON THE UNIT CIRCLE
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Copyright © University College London 2014. 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/r2 with s > 0.
author list (cited authors)
Erdélyi, T., Hardin, D. P., & Saff, E. B.