Resumen de On the degree of rational approximation of Markov functions on discrete sets
This article is devoted to results of rational approximation of the Markov function αˆ(z) = F dα(x) z − x , where α is a positive Borel measure with support supp α = F = [a, b] ⊂ (0, ∞) and dα/dx > 0 a.e. on F (with respect to the Lebesgue measure). We study asymptotic properties of the best uniform rational approximation of Markov functions ˆα on point systems EN ⊂ (−∞, 0) when the number of points N in the set EN and the degree of rational approximants n satisfy an asymptotic relation N/n → θ > 2 as n → ∞. The degree of rational approximation is described in terms of the solutions of certain logarithmic potential-theoretic problems, central among which is a minimal energy problem in the presence of an external field. We also investigate the limit distribution of poles of the best rational approximants and of points of Chebyshev alternance
