Determining Singularities Using Row Sequences of Padé-orthogonal Approximants

2013/06/02 by N. Bosuwan, Bosuwan, N., G. López Lagomasino +3
Mathematics · #41A27 #Complex Variables (math.CV) #FOS: Mathematics #Primary 30E10 #Secondary 41A21 #math.CV #msc:30E10 #msc:41A21 #msc:41A27

paper · pdf · doi:10.48550/arxiv.1306.0209

26 pages

arxiv created 2013/06/02 · arxiv updated 2013/06/04

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 the theorems of E. Fabry, R. de Montessus de Ballore, V.I. Buslaev, and S.P. Suetin.

Related

• Determining system poles using row sequences of orthogonal\n Hermite-Pad 'e approximants
• Inverse Theorem on Row Sequences of Linear Padé-orthogonal Approximation
• Direct and inverse results on row sequences of simultaneous Padé-Faber approximants
• Convergence of row sequences of simultaneous Fourier-Padé approximation
• On row sequences of Padé and Hermite-Padé approximation