Regular Article
The Distribution of Zeros and Poles of Asymptotically Extremal Rational Functions for Zolotarev's Problem☆

https://doi.org/10.1006/jath.2000.3551Get rights and content
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Abstract

We investigate the possible limit distributions of zeros and poles associated with ray sequences of rational functions that are asymptotically optimal for weighted Zolotarev problems. For disjoint compacta E1, E2 in the complex plane, the Zolotarev problem entails minimizing the ratio of the sup over E1 of the modulus of a weighted rational to its inf over E2. Potential theoretic tools are utilized in the analysis.

Keywords

Zolotarev problem
rational functions
asymptotic distributions
zeros and poles
potential theory

Cited by (0)

☆

Communicated by Doron, S. Lubinsky

f1

E-mail: [email protected]

f2

E-mail: [email protected]

1

The research of this author was supported, in part, by the U.S. National Science Foundation Research Grant DMS 9801677.

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