Fourier-Padé approximants for Nikishin systems

17 pages, no figures.-- MSC2000 codes: Primary: 30E10, 42C05; Secondary: 41A20.MR#: MR2519654Zbl#: Zbl 1175.30036We study type I Fourier–Padé approximation for certain systems of functions formed by the Cauchy transform of finite Borel measures supported on bounded intervals of the real line. This construction is similar to type I Hermite–Padé approximation. Instead of power series expansions of the functions in the system, we take their development in a series of orthogonal polynomials. We give the exact rate of convergence of the corresponding approximants. The answer is expressed in terms of the extremal solution of an associated vector-valued equilibrium problem for the logarithmic potential.The first author was supported by grants MTM 2006-13000-C03-02 and CCG06-UC3M/ESP-0690. The second received support from grant MTM 2006-13000-C03-03 of Ministerio de Ciencia y Tecnología, Spain.Publicad