2010/01/04 by U. Fidalgo Prieto, Prieto, U. Fidalgo, G. López Lagomasino +2
Computer Science · Mathematics · #30E10 #41A20 (Secondary) #42C05 (Primary) #Complex Variables (math.CV) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Matrix Theory and Algorithms #math.CV #msc:30E10 #msc:41A20 #msc:42C05
paper · pdf · doi:10.48550/arxiv.1001.0554
39 pages
arxiv created 2010/01/04 · openalex publication_date 2010/01/04 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
K. Mahler introduced the concept of perfect systems in the general theory he developed for the simultaneous Hermite-Pade approximation of analytic functions. We prove that Nikishin systems are perfect providing, by far, the largest class of systems of functions for which this important property holds. As consequences, in the context of Nikishin systems, we obtain: an extension of Markov's theorem to simultaneous Hermite-Pade approximation, a general result on the convergence of simultaneous quadrature rules of Gauss-Jacobi type, the logarithmic asymptotics of general sequences of multiple orthogonal polynomials, and an extension of the Denisov-Rakhmanov theorem for the ratio asymptotics of mixed type multiple orthogonal polynomials.