"On the Zeros of Weighted Faber Polynomials" by Matthew He
 

Mathematics Faculty Articles

On the Zeros of Weighted Faber Polynomials

Document Type

Article

Publication Date

1995

Publication Title

Indian Journal of Mathematics

ISSN

0019-5324

Volume

37

Issue/No.

2

First Page

79

Last Page

93

Abstract

Let E be a compact set in the complex plane C containing more than one point and having simply connected complement in the extended complex plane C¯¯¯¯. Denote by Fn(z;g) the Faber polynomial of degree n for E with weight function g(z). It is shown that if g(z) is an analytic function on C¯¯¯¯∖E with g(∞)>0 and singularity on ∂E then every point of ∂E is a limit point of the set of zeros of{Fn(z;g)}. To illustrate this result the author computes the zeros of the weighted Faber polynomials for an m-cusped hypocycloid (see also a paper by M. X. He and E. B. Saff [J. Approx. Theory 78 (1994), no. 3, 410–432; MR1292970] and the references therein).

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