On a problem by Steklov

2014/02/05 by A. Aptekarev, Alexander Ivanovich Aptekarev, S. Denisov +6
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.1402.1145

arXiv admin note: text overlap with arXiv:1308.6614. Several proofs are significantly simplified, typos fixed, references added

openalex publication_date 2014/02/05 · arxiv created 2015/07/27 · arxiv updated 2015/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain the sharp estimates on the growth of the uniform norm of orthonormal polynomials for measures satisfying the Steklov condition. This improves the earlier results by Rakhmanov and completely settles a problem by Steklov. The sharp estimates for the polynomial entropy in the Steklov class are obtained as well.

Citations

• The sharp estimates on the orthogonal polynomials from the Steklov class

Related

• The sharp estimates on the orthogonal polynomials from the Steklov class
• Continuity of weighted operators, Muckenhoupt A_p weights, and Steklov problem for orthogonal polynomials
• On the growth of the polynomial entropy integrals for the measures in the Szego class
• Remark on the formula by Rakhmanov and Steklov's conjecture
• Remark on the paper "Asymptotic behavior of polynomials orthonormal on a homogeneous set"