The Kadets $1/4$ theorem for polynomials

Abstract

We determine the maximal angular perturbation of the $(n+1)$th roots of unity permissible in the Marcinkiewicz-Zygmund theorem on $L^p$ means of polynomials of degree at most $n$. For $p=2$, the result is an analogue of the Kadets $1/4$ theorem on perturbation of Riesz bases of holomorphic exponentials.