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

R. K. Kovacheva

doi:10.4236/am.2015.65069

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

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DOI: 10.4236/am.2015.65069 2,751 Downloads 3,027 Views

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R. K. Kovacheva

Affiliation(s)

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

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.

Cite this paper

Kovacheva, R. (2015) Distribution of Points of Interpolation and of Zeros of Exactly Maximally Convergent Multipoint Padé Approximants. Applied Mathematics, 6, 737-744. doi: 10.4236/am.2015.65069.

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