Distribution of points of interpolation and of zeros of exact maximally convergent multipoint Padé approximants

Abstract

Given a regular compact set E in C, a unit measure µ supported by ∂E, a triangular point setn,m be the associated multipoint β− Padé approximant of order (n, m). We show that if the sequence π β,f n,m , n ∈ Λ, m− fixed, converges exact maximally to f , as n → ∞, n ∈ Λ inside the maximal domain of m− meromorphic continuability of f relatively to the measure µ, then the points β n,k are uniformly distributed on ∂E with respect to the measure µ as n ∈ Λ. Furthermore, a result about the zeros behavior of the exact maximally convergent sequence Λ is provided, under the condition that Λ is "dense enough."