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Asymptotic distribution of the zeros of Faber polynomials

Published online by Cambridge University Press:  24 October 2008

A. B. J. Kuijlaars  and
E. B. Saff
A. B. J. Kuijlaars
Affiliation:
Department of Mathematics and Computer Science, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands
E. B. Saff
Affiliation:
Institute for Constructive Mathematics, Department of Mathematics, University of South Florida, Tampa, FL 33620, U.S.A.
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Abstract

Using potential theoretic methods and exploiting the connection with eigenvalues of Toeplitz matrices, we investigate the limiting behaviour of zeros of Faber polynomials generated by a Laurent series. Our results build upon fundamental work of J. L. Ullman. For example, we show that if E is a compact set with simply connected complement and connected interior whose boundary is either (i) not a piecewise analytic curve or (ii) a piecewise analytic curve but with a singularity other than an outward cusp, then the equilibrium distribution for E is a limit measure of the sequence of normalized zero counting measures for the Faber polynomials associated with E.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 3 , November 1995 , pp. 437 - 447
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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