Dual mean value problem for complex polynomials

TL;DR

This paper investigates a dual extremal problem for complex polynomials related to the Smale mean value problem, providing degree-dependent estimates.

Contribution

It introduces a dual formulation of the mean value problem for polynomials and offers initial estimates based solely on polynomial degree.

Findings

Degree-dependent estimates for the dual mean value problem

Connection to the classical Smale mean value problem

Foundational step for further extremal polynomial analysis

Abstract

We consider an extremal problem for polynomials, which is dual to the well-known Smale mean value problem. We give a rough estimate depending only on the degree.