Determining Singularities Using Row Sequences of Pad\'e-orthogonal Approximants
Complex Variables
2013-06-04 v1
Abstract
Starting from the orthogonal polynomial expansion of a function 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 Thereby, we obtain analogues of the theorems of E. Fabry, R. de Montessus de Ballore, V.I. Buslaev, and S.P. Suetin.
Cite
@article{arxiv.1306.0209,
title = {Determining Singularities Using Row Sequences of Pad\'e-orthogonal Approximants},
author = {N. Bosuwan and G. López Lagomasino and E. B. Saff},
journal= {arXiv preprint arXiv:1306.0209},
year = {2013}
}
Comments
26 pages