Some properties of Faber-Walsh polynomials

2013/06/06 by Olivier Sète, Sète, Olivier
Computer Science · Mathematics · #30C20 #30E10 #30E15 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1306.1347

openalex publication_date 2013/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Walsh introduced a generalisation of Faber polynomials to certain compact sets which need not be connected. We derive several equivalent representations of these Faber-Walsh polynomials, analogous to representations of Faber polynomials. Some simple asymptotic properties of the Faber-Walsh polynomials on the complement of the compact set are established. We further show that suitably normalised Faber-Walsh polynomials are asymptotically optimal polynomials in the sense of [Eiermann and Niethammer 1983].

Citations

• �ber konforme Abbildungen, die gewisse Gebietsfunktionen in elementare Funktionen transformieren. I
• On canonical conformal maps of multiply connected domains
• A generalization of Faber's polynomials
• On the conformal mapping of multiply connected regions

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