arXiv subjects
Publications and source records attributed to A. Aptekarev.
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.
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.
We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arvesú et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the equilibrium problem with constrain to describe their zero distribution. Then analyzing the limiting behavior of the coefficients of the recurrence relations for Multiple Meixner polynomials we obtain the main term of their asymptotics.