The Kadets 1/4 theorem for polynomials

TL;DR

This paper investigates the maximum allowable angular deviation of roots of unity in polynomial mean theorems, extending Kadets 1/4 theorem to a new context, with specific results for p=2.

Contribution

It extends the Kadets 1/4 theorem to polynomial roots perturbations within the Marcinkiewicz-Zygmund framework, providing new bounds for angular perturbations.

Findings

Determines maximal angular perturbation for roots of unity in polynomial mean theorems.

Establishes an analogue of Kadets 1/4 theorem for p=2.

Provides bounds on perturbations preserving polynomial basis properties.

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.