Multipoint Rational Approximants with Preassigned Poles Original Research Article

Let μ be a finite positive Borel measure whose support S(μ) is a compact regular set contained in R. For a function of Markov type μ̂(z) = ∫S(μ) dμ(x)/(z − x), z ∈ C\S(μ), we consider multipoint Padé-type approximants (MPTAs), where some poles are preassigned and interpolation is carried out along a table of points contained in C̄\Co(S(μ)) which is symmetrical with respect to the real line. The main purpose of this paper is the study of the “exact rate of convergence” of the MPTAs to the function μ̂.