The sharp estimates on the orthogonal polynomials from the Steklov class
A. Aptekarev, S. Denisov, D. Tulyakov

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.
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Taxonomy
TopicsMathematical functions and polynomials · Mathematical Approximation and Integration · Mathematical Analysis and Transform Methods
