Determining singularities using rows of padé-orthogonal approximants

Nattapong Bosuwan; Guillermo López Lagomasino; Edward B. Saff

Determining singularities using rows of padé-orthogonal approximants

Nattapong Bosuwan
, Guillermo López Lagomasino
, Edward B. Saff

Vanderbilt University
Universidad Carlos III de Madrid

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

15 Citations (Scopus)

Abstract

Starting from the orthogonal polynomial expansion of a function F corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Padé-orthogonal approximants). We obtain both direct and inverse results relating the convergence of the poles of the approximants and the singularities of F. Thereby, we obtain analogues of theorems by E. Fabry, R. de Montessus de Ballore, V. I. Buslaev, and S. P. Suetin.

Original language	English
Pages (from-to)	179-208
Number of pages	30
Journal	Jaen Journal on Approximation
Volume	5
Issue number	2
Publication status	Published - Dec 2013
Externally published	Yes

Keywords

Fabry's theorem
Montessusde Ballore's theorem.
Orthogonal polynomials
Padé approximants

Cite this

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title = "Determining singularities using rows of pad{\'e}-orthogonal approximants",

abstract = "Starting from the orthogonal polynomial expansion of a function F corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Pad{\'e}-orthogonal approximants). We obtain both direct and inverse results relating the convergence of the poles of the approximants and the singularities of F. Thereby, we obtain analogues of theorems by E. Fabry, R. de Montessus de Ballore, V. I. Buslaev, and S. P. Suetin.",

keywords = "Fabry's theorem, Montessusde Ballore's theorem., Orthogonal polynomials, Pad{\'e} approximants",

author = "Nattapong Bosuwan and Lagomasino, \{Guillermo L{\'o}pez\} and Saff, \{Edward B.\}",

year = "2013",

month = dec,

language = "English",

volume = "5",

pages = "179--208",

journal = "Jaen Journal on Approximation",

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TY - JOUR

T1 - Determining singularities using rows of padé-orthogonal approximants

AU - Bosuwan, Nattapong

AU - Lagomasino, Guillermo López

AU - Saff, Edward B.

PY - 2013/12

Y1 - 2013/12

N2 - Starting from the orthogonal polynomial expansion of a function F corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Padé-orthogonal approximants). We obtain both direct and inverse results relating the convergence of the poles of the approximants and the singularities of F. Thereby, we obtain analogues of theorems by E. Fabry, R. de Montessus de Ballore, V. I. Buslaev, and S. P. Suetin.

AB - Starting from the orthogonal polynomial expansion of a function F corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Padé-orthogonal approximants). We obtain both direct and inverse results relating the convergence of the poles of the approximants and the singularities of F. Thereby, we obtain analogues of theorems by E. Fabry, R. de Montessus de Ballore, V. I. Buslaev, and S. P. Suetin.

KW - Fabry's theorem

KW - Montessusde Ballore's theorem.

KW - Orthogonal polynomials

KW - Padé approximants

UR - https://www.scopus.com/pages/publications/84893044375

M3 - Article

AN - SCOPUS:84893044375

SN - 1889-3066

VL - 5

SP - 179

EP - 208

JO - Jaen Journal on Approximation

JF - Jaen Journal on Approximation

IS - 2

ER -

Determining singularities using rows of padé-orthogonal approximants

Abstract

Keywords

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