INVERSE BERNSTEIN INEQUALITIES AND MIN–MAX–MIN PROBLEMS ON THE UNIT CIRCLE Academic Article uri icon

abstract

  • 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.

altmetric score

  • 0.5

author list (cited authors)

  • Erdélyi, T., Hardin, D. P., & Saff, E. B.

citation count

  • 5

publication date

  • August 2014

publisher