On a problem by Steklov

By Alexander I. Aptekarev, Sergey A. Denisov, D. N. Tulyakov. 2014

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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.

Subfields: Applied Mathematics, Numerical Analysis