Resumen de Determining singularities using rows of Padé-orthogonal approximants

Nattapong Bosuwan, Guillermo Tomás López Lagomasino , E. B. Saff

• 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.