The sharp estimates on the orthogonal polynomials from the Steklov class

TL;DR

This paper establishes precise lower bounds for the uniform norm and polynomial entropy of orthogonal polynomials within the Steklov class, advancing understanding of their extremal properties.

Contribution

It provides the first sharp bounds for orthogonal polynomials and their entropy in the Steklov class, filling a gap in the extremal analysis of these polynomials.

Findings

Sharp lower bound for the uniform norm of orthogonal polynomials in the Steklov class.

Sharp estimates for polynomial entropy in the Steklov class.

Enhanced understanding of extremal properties of orthogonal polynomials.

Abstract

We obtain the sharp lower bound for the uniform norm of the orthogonal polynomials in the Steklov class. We also prove the sharp estimates for the polynomial entropy in this class.