Distribution of Points of Interpolation and of Zeros of Exactly Maximally Convergent Multipoint Padé Approximants

Abstract

Given a regular compact set E in , a unit measure μ supported by , a triangular point set , and a function f , holomorphic on E , let π β,f n,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 , ∧ ∈ n,k are uniformly distributed on with respect to u as n ∈Λ . Furthermore, a result about the behavior of the zeros of the exact maximally convergent sequence Λ is provided, under the condition that Λ is “dense enough”.