Properties and examples of Faber--Walsh polynomials

Abstract

The Faber--Walsh polynomials are a direct generalization of the (classical) Faber polynomials from simply connected sets to sets with several simply connected components. In this paper we derive new properties of the Faber--Walsh polynomials, where we focus on results of interest in numerical linear algebra, and on the relation between the Faber--Walsh polynomials and the classical Faber and Chebyshev polynomials. Moreover, we present examples of Faber--Walsh polynomials for two real intervals as well as some non-real sets consisting of several simply connected components.

Minor rewording in Section 3, which now explicitly mentions the Bernstein-Walsh inequality

References in corpus (1)

• Numerical computation of the conformal map onto lemniscatic domains

Cited by in corpus (6)

• The AAA algorithm for rational approximation
• Fast and accurate computation of the logarithmic capacity of compact sets
• Numerical computation of the conformal map onto lemniscatic domains
• Walsh's Conformal Map onto Lemniscatic Domains for Several Intervals
• Walsh's Conformal Map onto Lemniscatic Domains for Polynomial Pre-images II
• The Complex Green's Function for Symmetric Sets