English

On a problem by Steklov

Classical Analysis and ODEs 2015-07-28 v2

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.

Keywords

Cite

@article{arxiv.1402.1145,
  title  = {On a problem by Steklov},
  author = {A. Aptekarev and S. Denisov and D. Tulyakov},
  journal= {arXiv preprint arXiv:1402.1145},
  year   = {2015}
}

Comments

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

R2 v1 2026-06-22T03:02:11.968Z