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

R. K. Kovacheva

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria.

DOI: 10.4236/am.2015.65069                

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”.

Keywords

Multipoint Padé Approximants, Maximal Convergence, Domain of m-Meromorphy

Conflicts of Interest

The authors declare no conflicts of interest.

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