Faber Polynomials for m-Fold Symmetric Domains

Authors

Matthew He, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

10-20-1994

Publication Title

Journal of Computational and Applied Mathematics

Keywords

Faber polynomials, m-fold symmetric domain, m-leaf lemniscates

ISSN

0377-0427

Volume

54

Issue/No.

3

First Page

313

Last Page

324

Abstract

The Faber polynomials for a region of the complex plane are of interest as a basis for polynomial approximations to analytic functions. In this paper we study the Faber polynomials associated with m-fold symmetric domains. Explicit formulae of Faber polynomials both for symmetric and nonsymmetric lemniscates are derived. In addition, we use a new determinant representation which relates the zeros of Faber polynomials to the eigenvalues of a certain matrix to compute the zeros of Faber polynomials for lemniscates.

NSUWorks Citation

He, Matthew, "Faber Polynomials for m-Fold Symmetric Domains" (1994). Mathematics Faculty Articles. 193.
https://nsuworks.nova.edu/math_facarticles/193

DOI

10.1016/0377-0427(94)90254-2