INVERSE BERNSTEIN INEQUALITIES AND MIN-MAX-MIN PROBLEMS ON THE UNIT CIRCLE
Academic Article
Overview
Research
Identity
Additional Document Info
Other
View All
Overview
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.