Fourier-Padé Approximants for Nikishin Systems Articles uri icon

publication date

  • August 2009

start page

  • 53

end page

  • 69

issue

  • 1

volume

  • 30

international standard serial number (ISSN)

  • 0176-4276

electronic international standard serial number (EISSN)

  • 1432-0940

abstract

  • We 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.