Fourier-Padé approximants for Nikishin systems

In this paper we study type I Fourier-Padé approximation for Nikishin systems. This construction is similar to that of Hermite-Padé approximation. Instead of considering power series expansions of the functions in the system, we take their expansion in a series of orthogonal polynomials. We obtain that the polynomials are type I multiple orthogonal polynomials with respect to a system of measures. We give the rate of convergence of these approximants for the system of Markov funtions associated to the Nikishin system. The answer is given in terms of the solution of the extremal solutions of certain vector valued equilibrium problems for the logarithmic potential.