Direct and inverse results for multipoint Hermite–Padé approximants

N. Bosuwan; G. López Lagomasino; Y. Zaldivar Gerpe

doi:10.1007/s13324-019-00316-8

Direct and inverse results for multipoint Hermite–Padé approximants

N. Bosuwan
, G. López Lagomasino
, Y. Zaldivar Gerpe

Mahidol University
CHE
Universidad Carlos III de Madrid

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Given a system of functions f= (f₁, … , f_d) analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement in the extended complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of row sequences of multipoint Hermite–Padé approximants under a general extremal condition on the table of interpolation points. The exact rate of convergence of these denominators is provided and the rate of convergence of the simultaneous approximants is estimated. These results allow us to detect the location of the poles of the system of functions which are in some sense closest to E.

Original language	English
Pages (from-to)	761-779
Number of pages	19
Journal	Analysis and Mathematical Physics
Volume	9
Issue number	2
DOIs	https://doi.org/10.1007/s13324-019-00316-8
Publication status	Published - 1 Jun 2019
Externally published	Yes

Keywords

Hermite–Padé approximation
Inverse type results
Montessus de Ballore theorem
Multipoint Padé approximation

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10.1007/s13324-019-00316-8

Cite this

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title = "Direct and inverse results for multipoint Hermite–Pad{\'e} approximants",

abstract = "Given a system of functions f= (f1, … , fd) analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement in the extended complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of row sequences of multipoint Hermite–Pad{\'e} approximants under a general extremal condition on the table of interpolation points. The exact rate of convergence of these denominators is provided and the rate of convergence of the simultaneous approximants is estimated. These results allow us to detect the location of the poles of the system of functions which are in some sense closest to E.",

keywords = "Hermite–Pad{\'e} approximation, Inverse type results, Montessus de Ballore theorem, Multipoint Pad{\'e} approximation",

author = "N. Bosuwan and \{L{\'o}pez Lagomasino\}, G. and \{Zaldivar Gerpe\}, Y.",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

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doi = "10.1007/s13324-019-00316-8",

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AU - Bosuwan, N.

AU - López Lagomasino, G.

AU - Zaldivar Gerpe, Y.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - Given a system of functions f= (f1, … , fd) analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement in the extended complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of row sequences of multipoint Hermite–Padé approximants under a general extremal condition on the table of interpolation points. The exact rate of convergence of these denominators is provided and the rate of convergence of the simultaneous approximants is estimated. These results allow us to detect the location of the poles of the system of functions which are in some sense closest to E.

AB - Given a system of functions f= (f1, … , fd) analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement in the extended complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of row sequences of multipoint Hermite–Padé approximants under a general extremal condition on the table of interpolation points. The exact rate of convergence of these denominators is provided and the rate of convergence of the simultaneous approximants is estimated. These results allow us to detect the location of the poles of the system of functions which are in some sense closest to E.

KW - Hermite–Padé approximation

KW - Inverse type results

KW - Montessus de Ballore theorem

KW - Multipoint Padé approximation

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SP - 761

EP - 779

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

IS - 2

ER -

Direct and inverse results for multipoint Hermite–Padé approximants

Abstract

Keywords

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