Inverse Bernstein inequalities and min-max-min problems on the unit circle
Metric Geometry
2015-09-23 v1
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 with
Cite
@article{arxiv.1307.4056,
title = {Inverse Bernstein inequalities and min-max-min problems on the unit circle},
author = {Tamás Erdélyi and Douglas P. Hardin and Edward B. Saff},
journal= {arXiv preprint arXiv:1307.4056},
year = {2015}
}