Direct and Inverse Results for Multipoint Hermite-Pade Approximants

2018/10/12 by Nattapong Bosuwan, Bosuwan, N., G. López Lagomasino +3
Mathematics · #30E10 #41A21 #41A28 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1810.07061

openalex publication_date 2018/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of multipoint Hermite-Pade approximants. The exact rate of convergence of these denominators and of the approximants themselves is given in terms of the analytic properties of the system of functions. These results allow to detect the location of the poles of the system of functions which are in some sense closest to E.

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