Constructive Approximation

, Volume 29, Issue 3, pp 421–448 | Cite as

On the Asymptotic Behavior of Faber Polynomials for Domains With Piecewise Analytic Boundary



Let φ(z) be an analytic function on a punctured neighborhood of ∞, where it has a simple pole. The nth Faber polynomial F n (z) (n=0,1,2,…) associated with φ is the polynomial part of the Laurent expansion at ∞ of [φ(z)] n . Assuming that ψ (the inverse of φ) conformally maps |w|>1 onto a domain Ω bounded by a piecewise analytic curve without cusps pointing out of Ω, and under an additional assumption concerning the “Lehman expansion” of ψ about those points of |w|=1 mapped onto corners of Ω, we obtain asymptotic formulas for F n that yield fine results on the limiting distribution of the zeros of Faber polynomials.


Faber polynomials Asymptotic behavior Zeros of polynomials Equilibrium measure Schwarz reflection principle Conformal map 

Mathematics Subject Classification (2000)

30E10 30E15 30C10 30C15 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MississippiUniversityUSA

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