Inverse Theorem on Row Sequences of Linear Padé-orthogonal Approximation

2014/11/25 by Nattapong Bosuwan, N. Bosuwan, Bosuwan, N. +2
Mathematics · #30E10 #41A21 #41A27 #Complex Variables (math.CV) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Mathematics and Applications #math.CV #msc:30E10 #msc:41A21 #msc:41A27

paper · pdf · doi:10.48550/arxiv.1411.7056

28 pages

arxiv created 2014/11/25 · openalex publication_date 2014/11/25 · arxiv updated 2014/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give necessary and sufficient conditions for the convergence with geometric rate of the denominators of linear Padé-orthogonal approximants corresponding to a measure supported on a general compact set in the complex plane. Thereby, we obtain an analogue of Gonchar's theorem on row sequences of Padé approximants.

Citations

• Extremal polynomials associated with a system of curves in the complex plane

Related

• Inverse results on row sequences of Hermite-Padé approximation
• On row sequences of Padé and Hermite-Padé approximation
• Direct and inverse results on row sequences of Hermite-Padé approximants
• Determining Singularities Using Row Sequences of Padé-orthogonal Approximants
• Direct and inverse results on row sequences of simultaneous Padé-Faber approximants