On the growth of the polynomial entropy integrals for the measures in the Szego class

TL;DR

This paper investigates the growth behavior of polynomial entropy integrals for measures in the Szego class, establishing sharp estimates for their potential unbounded growth.

Contribution

It provides the first sharp bounds on the growth of polynomial entropy integrals for Szego class measures, highlighting their possible unbounded nature.

Findings

Polynomial entropy integrals can grow for Szego class measures.

The derived estimates are proven to be sharp.

Growth behavior of these integrals is characterized precisely.

Abstract

For the polynomials orthogonal on the unit circle with respect to the measure from the Szego class we prove that the polynomial entropy integrals can grow. The estimate obtained is sharp.