English

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 FF 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.F. Thereby, we obtain analogues of the theorems of E. Fabry, R. de Montessus de Ballore, V.I. Buslaev, and S.P. Suetin.

Keywords

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

R2 v1 2026-06-22T00:26:34.516Z