Determining singularities using rows of Padé-orthogonal approximants

• Nattapong Bosuwan ^[1] ; Guillermo López Lagomasino ^[2] ; Edward B. Saff ^[1]
  1. [1] Vanderbilt University

     Vanderbilt University

     Estados Unidos

     
  2. [2] Universidad Carlos III de Madrid

     Universidad Carlos III de Madrid

     Madrid, España

     
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 5, Nº. 2, 2013, págs. 179-208
• Idioma: inglés
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• Resumen

  • 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.